ActuDistns
Functions for actuarial scientists

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R/richards.R

R/richards.R
In ActuDistns: Functions for actuarial scientists

Defines functions dgompertz dmakeham dperks dbeard dmakehamperks dmakehambeard dpareto dloglogistic dinvgauss dgengammad dlinear dkum dfrechet dhjorth daddweibull dschabe dlai dxie djshape dee dige dew del dburrx dgumbeld dexpext dchen dlgammad dmoe dmow dle dlr dlld dgpw dfw dgenF hgompertz hmakeham hperks hbeard hmakehamperks hmakehambeard hexponential hpareto hweibull hlogistic hloglogistic hnormal hlognormal hinvgauss hgamma hgengamma hlinear huniform hkum hfrechet hhjorth haddweibull hschabe hlai hxie hjshape hbeta hee hige hew hel hburrx hgumbel hexpext hchen hlgamma hmoe hmow hle hlr hll hgpw hfw hgenF igompertz imakeham iperks ibeard imakehamperks imakehambeard iexponential ipareto iweibull ilogistic iloglogistic inormal ilognormal iinvgauss igamma igengamma ilinear iuniform ikum ifrechet ihjorth iaddweibull ischabe ilai ixie ijshape ibeta iee iige iew iel iburrx igumbel iexpext ichen ilgamma imoe imow ile ilr ill igpw ifw igenF qgompertz qperks qbeard qexponential qpareto qweibull qlogistic qloglogis qnormal qlognormal qinversegaussian qgammad qgengammad qlinear quniform qkum qfrechet qhjorth qaddweibull qschabe qlai qxie qjshape qbetad qee qige qew qel qburrx qgumbeld qexpext qchen qlgammad qmoe qmow qle qlr qll qgpw qfw qgenF

Documented in daddweibull dbeard dburrx dchen dee del dew dexpext dfrechet dfw dgenF dgengammad dgompertz dgpw dgumbeld dhjorth dige dinvgauss djshape dkum dlai dle dlgammad dlinear dlld dloglogistic dlr dmakeham dmakehambeard dmakehamperks dmoe dmow dpareto dperks dschabe dxie haddweibull hbeard hbeta hburrx hchen hee hel hew hexpext hexponential hfrechet hfw hgamma hgenF hgengamma hgompertz hgpw hgumbel hhjorth hige hinvgauss hjshape hkum hlai hle hlgamma hlinear hll hlogistic hloglogistic hlognormal hlr hmakeham hmakehambeard hmakehamperks hmoe hmow hnormal hpareto hperks hschabe huniform hweibull hxie iaddweibull ibeard ibeta iburrx ichen iee iel iew iexpext iexponential ifrechet ifw igamma igenF igengamma igompertz igpw igumbel ihjorth iige iinvgauss ijshape ikum ilai ile ilgamma ilinear ill ilogistic iloglogistic ilognormal ilr imakeham imakehambeard imakehamperks imoe imow inormal ipareto iperks ischabe iuniform iweibull ixie qaddweibull qbeard qbetad qburrx qchen qee qel qew qexpext qexponential qfrechet qfw qgammad qgenF qgengammad qgompertz qgpw qgumbeld qhjorth qige qinversegaussian qjshape qkum qlai qle qlgammad qlinear qll qlogistic qloglogis qlognormal qlr qmoe qmow qnormal qpareto qperks qschabe quniform qweibull qxie 

#Gompertz probability density function

dgompertz=function(x,alpha=1,beta=1)
{
	ret = ifelse(x<=0 | alpha<=0 | beta<=0 ,
          NaN,alpha*exp(beta*x)*exp((1/beta)*alpha*(1-exp(beta*x))))
	return(ret)
}


#Makeham probability density function

dmakeham=function(x,alpha=1,beta=1,epsilon=1)
{
	ret = ifelse(x<=0 | alpha<=0 | beta<=0 | epsilon<=0,NaN,
          epsilon+alpha*exp(beta*x)*
          exp(-x*epsilon+(1/beta)*alpha*(1-exp(beta*x))))
	return(ret)
}



#Perks probability density function

dperks=function(x,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | beta<=0,NaN,
           alpha*exp(beta*x)*(1+alpha)/
           (1+alpha*exp(beta*x))**2)
	return(ret)
}



#Beard probability density function

dbeard=function(x,alpha=1,beta=1,rho=1)
{
	ret=ifelse(x<=0 | alpha<=0 | beta<=0 | rho<=0,NaN,
           alpha*exp(beta*x)*(1+alpha*rho)**(rho**(-1/beta))/
           (1+alpha*rho*exp(beta*x))**(1+rho**(-1/beta)))
	return(ret)
}



#Makeham-Perks probability density function

dmakehamperks=function(x,alpha=1,beta=1,epsilon=1)
{
	ret = ifelse(x<=0 | alpha<=0 | beta<=0 | epsilon<=0,NaN,
          (epsilon+alpha*exp(beta*x))/(1+alpha*exp(beta*x))*
          exp(-epsilon*x-(1/beta)*(epsilon-1)*log((1+alpha)/(1+alpha*exp(beta*x)))))
	return(ret)
}



#Makeham-Beard probability density function

dmakehambeard=function(x,alpha=1,beta=1,rho=1,epsilon=1)
{
	ret = ifelse(x<=0 | alpha<=0 | beta<=0 | epsilon<=0 | rho<=0,NaN,
          (epsilon+alpha*exp(beta*x))/(1+alpha*rho*exp(beta*x))*
          exp(-epsilon*x-(1/beta)*(1/rho)*(rho*epsilon-1)*log((1+alpha*rho)/(1+alpha*rho*exp(beta*x)))))
	return(ret)
}



#Exponential probability density function
#
#dexponential=function(x,alpha=1)
#{
#	ret	= ifelse(x<=0 | alpha<=0, NaN,alpha*exp(-alpha*x))
#	return(ret)
#}



#Pareto probability density function

dpareto=function(x,alpha=1,m=1)
{
	ret	= ifelse(x<=m | m<=0 | alpha<=0,NaN,(m/x)**(alpha)*alpha/x)
	return(ret)
}



#Weibull probability density function
#
#dweibull=function(x,alpha=1,sigma=1)
#{
#	ret	= ifelse(x<=0 | sigma<=0 | alpha<=0,NaN,
#           sigma*alpha**(-sigma)*x**(sigma-1)*exp(-(x/alpha)**sigma))
#	return(ret)
#}



#Logistic probability density function

#dlogistic=function(x,alpha=1,sigma=1)
#{
#	ret	= ifelse (sigma<=0,NaN,dlogis(x,location=alpha,scale=sigma))
#	return(ret)
#}
#
#The function {\sf dlogis} is  from the {\sf R} base package.



#Log-logistic probability density function

dloglogistic=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | sigma<=0, NaN,alpha*sigma*x**(sigma-1)*(1+alpha*x**sigma)**(-2))
	return(ret)
}



#Normal probability density function
#
#dnormal=function(x,alpha=1,sigma=1)
#{
#	ret	= ifelse (sigma<=0,NaN,dnorm(x,mean=alpha,sd=sigma))
#	return(ret)
#}
#
#The function {\sf dnorm} is  from the {\sf R} base package.


#Lognormal probability density function
#
#dlognormal=function(x,alpha=1,sigma=1)
#{
#	ret	= ifelse(x<=0 | sigma<=0, NaN,
#           dlnorm(x,meanlog=alpha,sdlog=sigma))
#	return(ret)
#}
#
#The function {\sf dlnorm} is  from the {\sf R} base package.


#Inverse-Gaussian probability density function

dinvgauss=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | sigma<=0, NaN,
           sqrt(sigma/(2*pi*x**3))*exp(-sigma*(x-alpha)**2/(2*alpha**2*x)))
	return(ret)
}



#Gamma probability density function
#
#dgammad=function(x,alpha=1,lambda=1)
#{
#	ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
#           dgamma(x,shape=lambda,scale=alpha))
#	return(ret)
#}
#
#The function {\sf dgamma} is  from the {\sf R} base package.



#Generalized-gamma probability density function

dgengammad=function(x,b=1,d=1,k=1)
{
	ret	= ifelse(x<=0 | b<=0 | d<=0 | k<=0, NaN,
            d*(b**(-d*k))*x**(d*k-1)*exp(-(x/b)**d)/gamma(k))           
	return(ret)
}


#Linear probability density function

dlinear=function(x,a=1,b=1)
{
	ret	= ifelse(x<=0 | a<0 | b<0 | a==0&b==0, NaN, (a+b*x)*exp(-a*x-b*x*x/2))
	return(ret)
}




#Uniform probability density function
#
#duniform=function(x,a=1,b=2)
#{
#	ret	= ifelse(b<=a | a<=0,NaN,1/(b-a))
#	return(ret)
#}




#Kumaraswamy probability density function

dkum=function(x,a=1,b=1)
{
	ret	= ifelse(x<=0 | x>=1 | a<=0 | b<=0,
           NaN,a*b*x**(a-1)*(1-x**a)**(b-1))
	return(ret)
}



#Gumbel II probability density function

dfrechet=function(x,a=1,b=1)
{
	ret	= ifelse(x<=0 | a<=0 | b<=0,
           NaN, a*b*x**(a-1)*exp(-b*x**(-a)))
	return(ret)
}



#Hjorth probability density function

dhjorth=function(x,delta=1,theta=1,beta=1)
{
	ret	= ifelse(x<=0 | delta<=0 | theta<=0 | beta<=0,
           NaN, ((1+beta*x)*delta*x+theta)*(1+beta*x)**(-1-theta/beta)*exp(-delta*x*x/2))
	return(ret)
}



#Additive Weibull probability density function

daddweibull=function(x,a=1,b=1,c=1,d=1)
{
	ret	= ifelse(x<=0 | a<=0 | b<=0 | c<=0 | d<=0,
           NaN, (a**b*b*x**{b-1}+c**d*d*x**{d-1})*exp(-(a*x)**b-(c*x)**d))
	return(ret)
}



#Schabe probability density function

dschabe=function(x,theta=1,gamma=0.5)
{
	ret	= ifelse(x>theta | gamma<=0 | gamma>=1 | theta<=0,
           NaN,(2*gamma+(1-gamma)*x/theta)/(theta*(gamma+x/theta)**2))
	return(ret)
}




#Lai probability density function

dlai=function(x,lambda=1,beta=1,nu=1)
{
	ret	= ifelse(x<=0 | lambda<=0 | beta<0 | nu<0,
           NaN,lambda*(beta+nu*x)*x**(beta-1)*exp(nu*x)*
           exp(-lambda*x**beta*exp(nu*x)))
	return(ret)
}




#Xie probability density function

dxie=function(x,lambda=1,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | lambda<=0 | alpha<=0 | beta<=0,
           NaN,
           lambda*beta*(x/alpha)**(beta-1)*
           exp((x/alpha)**beta+lambda*alpha*(1-exp((x/alpha)**beta))))
	return(ret)
}




#$J$-shaped probability density function

djshape=function(x,b=1,nu=1)
{
	y=1-x/b
    ret	= ifelse(y<=0 | y>=1 | b<=0 | nu<=0,
           NaN,(2/b)*nu*y*(1-y*y)**(nu-1))
	return(ret)
}




#Beta probability density function
#
#dbetad=function(x,a=1,b=1)
#{
#    ret	= ifelse(x<=0 | x>=1 | a<=0 | b<=0,
#           NaN,dbeta(x,shape1=a,shape2=b))
#	return(ret)
#}
#
#The function  {\sf dbeta} is  from the {\sf R} base package.



#Exponentiated exponential probability density function

dee=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN,dgen.exp(x,
           alpha=alpha,lambda=lambda))
	return(ret)
}

#The function {\sf dgen.exp} is  from the {\sf R} contributed package {\sf reliaR}.



#Inverse generalized exponential probability density function

dige=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN,dinv.genexp(x,
           alpha=alpha,lambda=lambda))
	return(ret)
}

#The function {\sf dinv.genexp} is  from the {\sf R} contributed package {\sf reliaR}.



#Exponentiated Weibull probability density function

dew=function(x,alpha=1,c=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | c<=0 | lambda<=0,
           NaN,lambda*dexpo.weibull(lambda*x,
           alpha=c,theta=alpha))
	return(ret)
}

#The function {\sf dexpo.weibull} is  from the {\sf R} contributed package {\sf reliaR}.



#Exponentiated logistic probability density function

del=function(x,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | beta<=0, NaN,
           dexpo.logistic(x,
           alpha=alpha,beta=beta))
	return(ret)
}

#The function {\sf dexpo.logistic} is  from the {\sf R} contributed package {\sf reliaR}.



#BurrX probability density function

dburrx=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dburrX(x,alpha=alpha,
           lambda=lambda))
	return(ret)
}

#The function {\sf dburrX} is  from the {\sf R} contributed package {\sf reliaR}.



#Gumbel probability density function

dgumbeld=function(x,mu=1,sigma=1)
{
    ret	= ifelse(sigma<=0, NaN,
           dgumbel(x,mu=mu,sigma=sigma))
	return(ret)
}

#The function {\sf dgumbel} is  from the {\sf R} contributed package {\sf reliaR}.



#Exponential extension probability density function

dexpext=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN, alpha*lambda*(1+lambda*x)**(alpha-1)*
           exp(1-(1+lambda*x)**alpha))
	return(ret)
}




#Chen probability density function

dchen=function(x,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | beta<=0 | lambda<=0,
           NaN, beta*lambda*
           x**(beta-1)*exp(x**beta)*exp(lambda-lambda*exp(x**beta)))
	return(ret)
}





#Loggamma probability density function

dlgammad=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=1 | alpha<=0 | lambda<=0, NaN,
           dlgamma(x,shapelog=alpha,
           ratelog=lambda))
	return(ret)
}

#The function {\sf dlgamma} is  from the {\sf R} contributed package {\sf actuar}.



#Marshall-Olkin exponential probability density function

dmoe=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN, lambda*
           exp(lambda*x)/
           (exp(lambda*x)-1+alpha)**2)
	return(ret)
}




#Marshall-Olkin Weibull probability density function

dmow=function(x,alpha=1,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | beta<=0 | lambda<=0,
           NaN, beta*lambda**beta*x**{beta-1}*
           exp((lambda*x)**beta)/
           (exp((lambda*x)**beta)-1+alpha)**2)
	return(ret)
}




#Logistic exponential probability density function

dle=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dlogis.exp(x,
           alpha=alpha,lambda=lambda))
	return(ret)
}

#The function {\sf dlogis.exp} is  from the {\sf R} contributed package {\sf reliaR}.



#Logistic Rayleigh probability density function

dlr=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dlogis.rayleigh(x,
           alpha=alpha,lambda=lambda))
	return(ret)
}

#The function {\sf dlogis.rayleigh} is  from the {\sf R} contributed package {\sf reliaR}.



#Loglog probability density function

dlld=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN,alpha*log(lambda)*
           x**(alpha-1)*lambda**(x**alpha)*exp(1-lambda**(x**alpha)))
	return(ret)
}




#Generalized power Weibull probability density function

dgpw=function(x,alpha=1,theta=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | theta<=0,
           NaN,alpha*theta*x**{alpha-1}*
           (1+x**alpha)**{theta-1}*exp(1-(1+x**alpha)**theta))
	return(ret)
}




#Flexible Weibull probability density function

dfw=function(x,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | beta<=0,
           NaN,(alpha+beta/(x*x))*
           exp(alpha*x-beta/x)*exp(-exp(alpha*x-beta/x)))
	return(ret)
}




#Generalized $F$ probability density function

dgenF=function(x,beta=0,sigma=1,m1=1,m2=1)
{
    ret	= ifelse(x<=0 | sigma<=0 | m1<=0 | m2<=0,
           NaN,exp(-beta*m1/sigma)*(m1/m2)**m1*x**(m1/sigma-1)/(sigma*beta(m1,m2)*(1+(m1/m2)*(exp(-beta)*x)**(1/sigma))**(m1+m2)))
	return(ret)
}



#Gompertz hazard rate function

hgompertz=function(x,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | beta<=0,
           NaN,alpha*exp(beta*x))
	return(ret)
}



#Makeham hazard rate function

hmakeham=function(x,alpha=1,beta=1,epsilon=1)
{
	ret	=ifelse(x<=0 | alpha<=0 | beta<=0 | epsilon <=0,NaN,
          epsilon+alpha*exp(beta*x))
	return(ret)
}



#Perks hazard rate function

hperks=function(x,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | beta<=0,NaN,
           alpha*exp(beta*x) /
           (1+alpha*exp(beta*x)))
	return(ret)
}



#Beard hazard rate function

hbeard=function(x,alpha=1,beta=1,rho=1)
{
	ret=ifelse(x<=0 | alpha<=0 | beta<=0 | rho<=0,NaN,
           alpha*exp(beta*x) /
           (1+alpha*rho*exp(beta*x)))
	return(ret)
}



#Makeham-Perks hazard rate function

hmakehamperks=function(x,alpha=1,beta=1,epsilon=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | beta<=0 | epsilon<=0,
           NaN,(epsilon+alpha*exp(beta*x)) /
           (1+alpha*exp(beta*x)))
	return(ret)
}



#Makeham-Beard hazard rate function

hmakehambeard=function(x,alpha=1,beta=1,rho=1,epsilon=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | beta<=0 | rho<=0 | epsilon<=0,
           NaN,(epsilon+alpha*exp(beta*x)) /
           (1+alpha*rho*exp(beta*x)))
	return(ret)
}



#Exponential hazard rate function

hexponential=function(x,alpha=1)
{
	ret	= ifelse(x<=0 | alpha<=0, NaN,alpha)
	return(ret)
}



#Pareto hazard rate function

hpareto=function(x,alpha=1,m=1)
{
	ret	= ifelse(x<=m | m<=0 | alpha<=0,NaN,alpha/x)
	return(ret)
}



#Weibull hazard rate function

hweibull=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | sigma<=0 | alpha<=0,NaN,
           alpha*x**(alpha-1)/sigma**alpha)
	return(ret)
}



#Logistic hazard rate function

hlogistic=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(sigma<=0,NaN,1 / (sigma*
           (1+exp( -(x-alpha)/sigma))))
	return(ret)
}



#Log-logistic hazard rate function

hloglogistic=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | sigma<=0 | alpha<=0, NaN,
                alpha*sigma*x**(sigma-1)/(1+alpha*x**sigma))
	return(ret)
}



#Normal hazard rate function

hnormal=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | sigma<=0,NaN,dnorm(x,mean=alpha,sd=sigma) /
          (1-pnorm(x,mean=alpha,sd=sigma)))
	return(ret)
}

#The functions {\sf dnorm} and {\sf pnorm} are  from the {\sf R} base package.


#Lognormal hazard rate function

hlognormal=function(x,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | sigma<=0, NaN,
           dlnorm(x,meanlog=alpha,sdlog=sigma) /
           (1-plnorm(x,meanlog=alpha,sdlog=sigma)))
	return(ret)
}

#The functions {\sf dlnorm} and {\sf plnorm} are  from the {\sf R} base package.


#Inverse-Gaussian hazard rate function

hinvgauss=function(x,alpha=1,sigma=1)
{
	ret=NaN
        if (x>0&alpha>0&sigma>0)
        {tt=sqrt(sigma/(2*pi*x**3))*exp(-sigma*(x-alpha)**2/(2*alpha**2*x))
        tt2=pnorm(sqrt(sigma/x)*(x/alpha-1))+exp(2*sigma/alpha)*pnorm(-sqrt(sigma/x)*(x/alpha+1))
        ret=tt/(1-tt2)}
	return(ret)
}

#The function {\sf pnorm} is from the {\sf R} base package.


#Gamma hazard rate function

hgamma=function(x,alpha=1,lambda=1)
{
	ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dgamma(x,shape=lambda,scale=alpha) /
           (1-pgamma(x,shape=lambda,scale=alpha)))
	return(ret)
}

#The functions {\sf dgamma} and {\sf pgamma} are  from the {\sf R} base package.



#Generalized-gamma hazard rate function

hgengamma=function(x,b=1,d=1,k=1)
{
	ret	= ifelse(x<=0 | b<=0 | d<=0 | k<=0, NaN,
          d*(b**(-d*k))*x**(d*k-1)*exp(-(x/b)**d)/(gamma(k)*(1-pgamma((x/b)**d,shape=k))))
	return(ret)
}

#The function {\sf pgamma} is from the {\sf R} base package.


#Linear hazard rate function

hlinear=function(x,a=1,b=1)
{
	ret	= ifelse(x<=0 | a<0 | b<0 | a==0&b==0, NaN, a+b*x)
	return(ret)
}




#Uniform hazard rate function

huniform=function(x,a=1,b=2)
{
	ret	= ifelse(x<=a | x>=b | b<=a | a<=0,
           NaN, 1/(b-x))
	return(ret)
}




#Kumaraswamy hazard rate function

hkum=function(x,a=1,b=1)
{
	ret	= ifelse(x<=0 | x>=1 | a<=0 | b<=0,
           NaN,a*b*x**(a-1)/(1-x**a))
	return(ret)
}



#Gumbel II hazard rate function

hfrechet=function(x,a=1,b=1)
{
	ret	= ifelse(x<=0 | a<=0 | b<=0,
           NaN, a*b*x**(a-1))
	return(ret)
}



#Hjorth hazard rate function

hhjorth=function(x,delta=1,theta=1,beta=1)
{
	ret	= ifelse(x<=0 | delta<=0 | theta<=0 | beta<=0,
           NaN, delta*x+theta/(1+beta*x))
	return(ret)
}



#Additive Weibull hazard rate function

haddweibull=function(x,a=1,b=1,c=1,d=1)
{
	ret	= ifelse(x<=0 | a<=0 | b<=0 | c<=0 | d<=0,
           NaN, a**b*b*x**{b-1}+
           c**d*d*x**{d-1})
	return(ret)
}



#Schabe hazard rate function

hschabe=function(x,theta=1,gamma=0.5)
{
	ret	= ifelse(x>theta | gamma<=0 | gamma>=1 | theta<=0,
           NaN,1/(theta*gamma+x)+
           1/(theta-x))
	return(ret)
}




#Lai hazard rate function

hlai=function(x,lambda=1,beta=1,nu=1)
{
	ret	= ifelse(x<=0 | lambda<=0 | beta<0 | nu<0,
           NaN,lambda*(beta+nu*x)*
           x**(beta-1)*exp(nu*x))
	return(ret)
}




#Xie hazard rate function

hxie=function(x,lambda=1,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | lambda<=0 | alpha<=0 | beta<=0,
           NaN,
           lambda*beta*(x/alpha)**(beta-1)*exp((x/alpha)**beta))
	return(ret)
}




#$J$-shaped hazard rate function

hjshape=function(x,b=1,nu=1)
{
	y=1-x/b
    ret	= ifelse(y<=0 | y>=1 | b<=0 | nu<=0,
           NaN,(2/b)*nu*y*(1-y*y)**(nu-1)/
           (1-(1-y*y)**nu))
	return(ret)
}




#Beta hazard rate function

hbeta=function(x,a=1,b=1)
{
    ret	= ifelse(x<=0 | x>=1 | a<=0 | b<=0,
           NaN,dbeta(x,shape1=a,shape2=b)/
           (1-pbeta(x,shape1=a,shape2=b)))
	return(ret)
}

#The functions  {\sf dbeta} and {\sf pbeta} are  from the {\sf R} base package.



#Exponentiated exponential hazard rate function

hee=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN,dgen.exp(x,
           alpha=alpha,lambda=lambda)/
           (1-pgen.exp(x,
           alpha=alpha,lambda=lambda)))
	return(ret)
}

#The functions {\sf dgen.exp} and {\sf pgen.exp} are  from the {\sf R} contributed package {\sf reliaR}.



#Inverse generalized exponential hazard rate function

hige=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN,dinv.genexp(x,
           alpha=alpha,lambda=lambda)/
           (1-pinv.genexp(x,
           alpha=alpha,lambda=lambda)))
	return(ret)
}

#The functions {\sf dinv.genexp} and {\sf pinv.genexp} are  from the {\sf R} contributed package {\sf reliaR}.



#Exponentiated Weibull hazard rate function

hew=function(x,alpha=1,c=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | c<=0 | lambda<=0,
           NaN,lambda*dexpo.weibull(lambda*x,
           alpha=c,theta=alpha)/
           (1-pexpo.weibull(lambda*x,
           alpha=c,theta=alpha)))
	return(ret)
}

#The functions {\sf dexpo.weibull} and {\sf pexpo.weibull} are  from the {\sf R} contributed package {\sf reliaR}.



#Exponentiated logistic hazard rate function

hel=function(x,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | beta<=0, NaN,
           dexpo.logistic(x,
           alpha=alpha,beta=beta)/
           (1-pexpo.logistic(x,
           alpha=alpha,beta=beta)))
	return(ret)
}

#The functions {\sf dexpo.logistic} and {\sf pexpo.logistic} are  from the {\sf R} contributed package {\sf reliaR}.


#BurrX hazard rate function

hburrx=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dburrX(x,alpha=alpha,
           lambda=lambda)/
           (1-pburrX(x,alpha=alpha,
           lambda=lambda)))
	return(ret)
}

#The functions {\sf dburrX} and {\sf pburrX} are  from the {\sf R} contributed package {\sf reliaR}.



#Gumbel hazard rate function

hgumbel=function(x,mu=1,sigma=1)
{
    ret	= ifelse(sigma<=0, NaN,
           dgumbel(x,mu=mu,sigma=sigma)/
           (1-pgumbel(x,mu=mu,sigma=sigma)))
	return(ret)
}

#The functions {\sf dgumbel} and {\sf pgumbel} are  from the {\sf R} contributed package {\sf reliaR}.


#Exponential extension hazard rate function

hexpext=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN, alpha*lambda*
           (1+lambda*x)**(alpha-1))
	return(ret)
}




#Chen hazard rate function

hchen=function(x,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | beta<=0 | lambda<=0,
           NaN, beta*lambda*
           x**(beta-1)*exp(x**beta))
	return(ret)
}





#Loggamma hazard rate function

hlgamma=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=1 | alpha<=0 | lambda<=0, NaN,
           dlgamma(x,shapelog=alpha,
           ratelog=lambda)/
           (1-plgamma(x,shapelog=alpha,
           ratelog=lambda)))
	return(ret)
}

#The functions {\sf dlgamma} and {\sf plgamma} are  from the {\sf R} contributed package {\sf actuar}.


#Marshall-Olkin exponential hazard rate function

hmoe=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN, lambda*
           exp(lambda*x)/
           (exp(lambda*x)-1+alpha))
	return(ret)
}




#Marshall-Olkin Weibull hazard rate function

hmow=function(x,alpha=1,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | beta<=0 | lambda<=0,
           NaN, beta*
           lambda**beta*x**{beta-1}*
           exp((lambda*x)**beta)/
           (exp((lambda*x)**beta)-1+alpha))
	return(ret)
}




#Logistic exponential hazard rate function

hle=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dlogis.exp(x,
           alpha=alpha,lambda=lambda)/
           (1-plogis.exp(x,
           alpha=alpha,lambda=lambda)))
	return(ret)
}

#The functions {\sf dlogis.exp} and {\sf plogis.exp} are  from the {\sf R} contributed package {\sf reliaR}.



#Logistic Rayleigh hazard rate function

hlr=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0, NaN,
           dlogis.rayleigh(x,
           alpha=alpha,lambda=lambda)/
           (1-plogis.rayleigh(x,
           alpha=alpha,lambda=lambda)))
	return(ret)
}

#The functions {\sf dlogis.rayleigh} and {\sf plogis.rayleigh} are  from the {\sf R} contributed package {\sf reliaR}.



#Loglog hazard rate function

hll=function(x,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | lambda<=0,
           NaN,alpha*log(lambda)*
           x**(alpha-1)*
           lambda**(x**alpha))
	return(ret)
}




#Generalized power Weibull hazard rate function

hgpw=function(x,alpha=1,theta=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | theta<=0,
           NaN,alpha*theta*x**{alpha-1}*
           (1+x**alpha)**{theta-1})
	return(ret)
}




#Flexible Weibull hazard rate function

hfw=function(x,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | alpha<=0 | beta<=0,
           NaN,(alpha+beta/(x*x))*
           exp(alpha*x-beta/x))
	return(ret)
}




#Generalized $F$ hazard rate function

hgenF=function(x,beta=0,sigma=1,m1=1,m2=1)
{
    ret	= ifelse(x<=0 | sigma<=0 | m1<=0 | m2<=0,
           NaN,exp(-beta*m1/sigma)*(m1/m2)**m1*x**(m1/sigma-1)/
           (sigma*beta(m1,m2)*(1+(m1/m2)*(exp(-beta)*x)**(1/sigma))**(m1+m2)*
           (1-pbeta(m1*(exp(-beta)*x)**(1/sigma)/(m2+m1*(exp(-beta)*x)**(1/sigma)),shape1=m1,shape2=m2))))
	return(ret)
}

#The function {\sf pbeta} is  from the {\sf R} base package.



#Gompertz integrated hazard rate function

igompertz=function(x,t=1,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | beta<=0,
           NaN, (1/beta)*
           (exp(beta*t)-1)*
           alpha*exp(beta*x))
	return(ret)
}



#Makeham integrated hazard rate function

imakeham=function(x,t=1,alpha=1,beta=1,epsilon=1)
{
	ret	=ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | beta<=0 | epsilon<=0,
          NaN,t*epsilon+(1/beta)*
          (exp(beta*t)-1)*
          alpha*exp(beta*x))
	return(ret)
}



#Perks integrated hazard rate function

iperks=function(x,t=1,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | beta<=0,
           NaN, (1/beta)*log(
           (1+alpha*exp(beta*(x+t))) /
           (1+alpha*exp(beta*x))))
	return(ret)
}



#Beard integrated hazard rate function

ibeard=function(x,t=1,alpha=1,beta=1,rho=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | beta<=0 | rho<=0,
           NaN, (1/beta)*(1/rho)*
           log((1+alpha*rho*exp(beta*(x+t))) /
           (1+alpha*rho*exp(beta*x))))
	return(ret)
}



#Makeham-Perks integrated hazard rate function

imakehamperks=function(x,t=1,alpha=1,beta=1,epsilon=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | beta<=0 | epsilon<=0,
           NaN, t*epsilon+(1/beta)*
           (1-epsilon)*
           log((1+alpha*exp(beta*(x+t))) /
           (1+alpha*exp(beta*x))))
	return(ret)
}



#Makeham-Beard integrated hazard rate function

imakehambeard=function(x,t=1,alpha=1,beta=1,rho=1,epsilon=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | beta<=0 | rho<=0 | epsilon<=0,
           NaN, t*epsilon+(1/beta)*
           (1/rho-epsilon)*
           log((1+alpha*rho*exp(beta*(x+t))) /
           (1+alpha*rho*exp(beta*x))))
	return(ret)
}



#Exponential integrated hazard rate function

iexponential=function(x,t=1,alpha=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0,
           NaN,t*alpha)
	return(ret)
}



#Pareto integrated hazard rate function

ipareto=function(x,t=1,alpha=1,m=1)
{
	ret	= ifelse(x<=m | t<=0 | m<=0 | length(x)!=length(t) | alpha<=0,
           NaN,alpha*log(1+t/x))
	return(ret)
}



#Weibull integrated hazard rate function

iweibull=function(x,t=1,alpha=1,sigma=1)
{
	ret=ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | sigma<=0,
                   NaN,((x+t)**sigma-x**sigma)/alpha**sigma)
        return(ret)
}



#Logistic integrated hazard rate function

ilogistic=function(x,t=1,alpha=1,sigma=1)
{
	ret	= ifelse(length(x)!=length(t) | sigma<=0,NaN,
           log((1 + exp((x+t-alpha)/sigma)) /
           (1 + exp((x-alpha)/sigma))))
	return(ret)
}



#Log-logistic integrated hazard rate function

iloglogistic=function(x,t=1,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | sigma<=0,
           NaN, log(
           (1+alpha*(x+t)**sigma) /
           (1+alpha*x**sigma)))
	return(ret)
}




#Normal integrated hazard rate function

inormal=function(x,t=1,alpha=1,sigma=1)
{
	ret	= ifelse(length(x)!=length(t) | sigma<=0,NaN,
           log((1-pnorm((x-alpha)/sigma)) /
           (1-pnorm((x+t-alpha)/sigma))))
	return(ret)
}

#The function {\sf pnorm} is  from the {\sf R} base package.


#Lognormal integrated hazard rate function

ilognormal=function(x,t=1,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | sigma<=0,
           NaN, log(
           (1-plnorm((log(x)-alpha)/sigma)) /
           (1-plnorm((log(x+t)-alpha)/sigma))))
	return(ret)
}

#The function {\sf plnorm} is  from the {\sf R} base package.



#Inverse-Gaussian integrated hazard rate function

iinvgauss=function(x,t=1,alpha=1,sigma=1)
{
	ret=NaN
        if (x>0&t>0&length(x)==length(t)&alpha>0&sigma>0)
        {tt=pnorm(sqrt(sigma/x)*(x/alpha-1))+exp(2*sigma/alpha)*pnorm(-sqrt(sigma/x)*(x/alpha+1))
        tt2=pnorm(sqrt(sigma/(x+t))*((x+t)/alpha-1))+exp(2*sigma/alpha)*pnorm(-sqrt(sigma/(x+t))*((x+t)/alpha+1))
        ret=log((1-tt)/(1-tt2))}
	return(ret)
}

#The function {\sf pnorm} is from the {\sf R} base package.


#Gamma integrated hazard rate function

igamma=function(x,t=1,alpha=1,lambda=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | lambda<=0,
           NaN, log((1-pgamma(x,shape=lambda,scale=alpha)) /
           (1-pgamma(x+t,shape=lambda,scale=alpha))))
	return(ret)
}

#The function {\sf pgamma} is  from the {\sf R} base package.


#Generalized-gamma integrated hazard rate function

igengamma=function(x,t=1,b=1,d=1,k=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | b<=0 | d<=0 | k<=0,
           NaN, log((1-pgamma((x/b)**d,shape=k))/(1-pgamma(((x+t)/b)**d,shape=k))))
	return(ret)
}

#The function {\sf pgamma} is  from the {\sf R} base package.


#Linear integrated hazard rate function

ilinear=function(x,t=1,a=1,b=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | a<0 | b<0 | a==0&b==0,
           NaN, (a+b*x)*t+b*t*t/2)
	return(ret)
}



#Uniform integrated hazard rate function

iuniform=function(x,t=1,a=0,b=1)
{
	ret	= ifelse(x<=a | x>=b | t<=0 | length(x)!=length(t) | b<=a | a<=0,
           NaN,log((b-x)/(b-x-t)))
	return(ret)
}



#Kumaraswamy integrated hazard rate function

ikum=function(x,t=1,a=0,b=1)
{
	ret	= ifelse(x<=0 | x>=1 | t<=0 | t>=1 |
           length(x)!=length(t) | a<=0 | b<=0,
           NaN,b*log((1-x**a)/(1-(x+t)**a)))
	return(ret)
}




#Gumbel II integrated hazard rate function

ifrechet=function(x,t=1,a=1,b=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | a<=0 | b<=0,
           NaN, b*(x**(-a-1)-(x+t)**(-a-1)))
	return(ret)
}




#Hjorth integrated hazard rate function

ihjorth=function(x,t=1,delta=1,theta=1,beta=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | delta<=0 | theta<=0 | beta<=0,
           NaN, delta*x*t+
           delta*t*t/2+(theta/beta)*
           log(1+beta*t/(1+beta*x)))
	return(ret)
}



#Additive Weibull integrated hazard rate function

iaddweibull=function(x,t=1,a=1,b=1,c=1,d=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | a<=0 | b<=0 | c<=0 | d<=0,
           NaN, a**b*(x+t)**b+c**d*(x+t)**d)
	return(ret)
}




#Schabe integrated hazard rate function

ischabe=function(x,t=1,theta=1,gamma=0.5)
{
	ret	= ifelse(x>theta | t>theta | length(x)!=length(t)
           | theta<=0 | gamma<=0 | gamma>=1,
           NaN,log(1+t/(theta*gamma+x))-
           log(1-t/(theta-x)))
	return(ret)
}




#Lai integrated hazard rate function

ilai=function(x,t=1,lambda=1,beta=1,nu=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) |
           lambda<=0 | beta<0 | nu<0,NaN,lambda*(-x**beta*
           genhypergeo(U=beta,L=1+beta,z=nu*x)
           +(x+t)**beta*
           genhypergeo(U=beta,L=1+beta,z=nu*(x+t))
           -(nu/(beta+1))*x**(beta+1)*
           genhypergeo(U=1+beta,L=2+beta,z=nu*x)
           +(nu/(beta+1))*(x+t)**(beta+1)*
           genhypergeo(U=1+beta,L=2+beta,z=nu*(x+t))))
	return(ret)
}

#The function {\sf genhypergeo} is  from the {\sf R} contributed package {\sf hypergeo}.


#Xie integrated hazard rate function

ixie=function(x,t=1,lambda=1,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | lambda<=0 | alpha<=0 | beta<=0,
           NaN,lambda*alpha*
           (exp(((x+t)/alpha)**beta)-
           exp((x/alpha)**beta)))
	return(ret)
}




#$J$-shaped integrated hazard rate function

ijshape=function(x,t=1,b=1,nu=1)
{
	y1=1-x/b
    y2=1-(x+t)/b
    ret	= ifelse(y1<=0 | y1>=1 | t<=0 | t>=b
           | length(x)!=length(t) | b<=0 | nu<=0,
           NaN,log((1-(1-y1*y1)**nu)/
           (1-(1-y2*y2)**nu)))
	return(ret)
}




#Beta integrated hazard rate function

ibeta=function(x,t=1,a=1,b=1)
{
    ret	= ifelse(x<=0 | x>=1 | t<=0 | t>=1 |
           length(x)!=length(t) | a<=0 | b<=0,NaN,
           log((1-pbeta(x,shape1=a,shape2=b))/
           (1-pbeta(x+t,shape1=a,shape2=b))))
	return(ret)
}

#The function  {\sf pbeta} is  from the {\sf R} base package.

#Exponentiated exponential integrated hazard rate function

iee=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) | alpha<=0 | lambda<=0,
           NaN,-log((1-pgen.exp(x+t,
           alpha=alpha,lambda=lambda))/
           (1-pgen.exp(x,
           alpha=alpha,lambda=lambda))))
	return(ret)
}

#The function {\sf pgen.exp} is  from the {\sf R} contributed package {\sf reliaR}.


#Inverse generalized exponential integrated hazard rate function

iige=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) |
           alpha<=0 | lambda<=0,NaN,-log((1-pinv.genexp(x+t,
           alpha=alpha,lambda=lambda))/
           (1-pinv.genexp(x,
           alpha=alpha,lambda=lambda))))
	return(ret)
}

#The function {\sf pinv.genexp} is  from the {\sf R} contributed package {\sf reliaR}.




#Exponentiated Weibull integrated hazard rate function

iew=function(x,t=1,alpha=1,c=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | c<=0 | lambda<=0,
           NaN,-log((1-pexpo.weibull(lambda*(x+t),
           alpha=c,theta=alpha))/
           (1-pexpo.weibull(lambda*x,
           alpha=c,theta=alpha))))
	return(ret)
}

#The function {\sf pexpo.weibull} is  from the {\sf R} contributed package {\sf reliaR}.



#Exponentiated logistic integrated hazard rate function

iel=function(x,t=1,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | beta<=0,
           NaN,log((1-pexpo.logistic(x,
           alpha=alpha,beta=beta))/
           (1-pexpo.logistic(x+t,
           alpha=alpha,beta=beta))))
	return(ret)
}

#The function {\sf pexpo.logistic} is  from the {\sf R} contributed package {\sf reliaR}.



#BurrX integrated hazard rate function

iburrx=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | lambda<=0, NaN,-log((1-pburrX(x+t,
           alpha=alpha,lambda=lambda))/
           1-pburrX(x,
           alpha=alpha,lambda=lambda)))
	return(ret)
}

#The function {\sf pburrX} is  from the {\sf R} contributed package {\sf reliaR}.


#Gumbel integrated hazard rate function

igumbel=function(x,t=1,mu=1,sigma=1)
{
    ret	= ifelse(length(x)!=length(t) | sigma<=0,NaN,
           -log((1-pgumbel(x+t,
           mu=mu,sigma=sigma))/
           (1-pgumbel(x,
           mu=mu,sigma=sigma))))
	return(ret)
}

#The function {\sf pgumbel} is  from the {\sf R} contributed package {\sf reliaR}.



#Exponential extension integrated hazard rate function

iexpext=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<= 0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | lambda<=0,NaN,
           (1+lambda*x+lambda*t)**alpha-
           (1+lambda*x)**alpha)
	return(ret)
}




#Chen integrated hazard rate function

ichen=function(x,t=1,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) |
           beta<=0 | lambda<=0,
           NaN, lambda*
           (exp((x+t)**beta)-exp(x**beta)))
	return(ret)
}


#Loggamma integrated hazard rate function

ilgamma=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=1 | t<=0 | length(x)!=length(t)
           | alpha<=0 | lambda<=0,
           -log((1-plgamma(x+t,shapelog=alpha,
           ratelog=lambda))/
           (1-plgamma(x,shapelog=alpha,
           ratelog=lambda))))
	return(ret)
}

#The function {\sf plgamma} is  from the {\sf R} contributed package {\sf actuar}.



#Marshall-Olkin exponential integrated hazard rate function

imoe=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | lambda<=0,
           NaN, log((exp(lambda*(x+t))-1+alpha)/
           (exp(lambda*x)-1+alpha)))
	return(ret)
}




#Marshall-Olkin Weibull integrated hazard rate function

imow=function(x,t=1,alpha=1,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | beta<=0 | lambda<=0,
           NaN, log(
           (exp((lambda*(x+t))**beta)-1+alpha)/
           (exp((lambda*x)**beta)-1+alpha)))
	return(ret)
}


#Logistic exponential integrated hazard rate function

ile=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | lambda<=0,
           NaN,log((1-plogis.exp(x,
           alpha=alpha,lambda=lambda))/
           (1-plogis.exp(x+t,
           alpha=alpha,lambda=lambda))))
	return(ret)
}

#The function {\sf plogis.exp} is  from the {\sf R} contributed package {\sf reliaR}.


#Logistic Rayleigh integrated hazard rate function

ilr=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | lambda<=0,
           NaN,log((1-plogis.rayleigh(x,
           alpha=alpha,lambda=lambda))/
           (1-plogis.rayleigh(x+t,
           alpha=alpha,lambda=lambda))))
	return(ret)
}

#The function {\sf plogis.rayleigh} is  from the {\sf R} contributed package {\sf reliaR}.


#Loglog integrated hazard rate function

ill=function(x,t=1,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t) |
           alpha<=0 | lambda<=0,
           NaN,lambda**((x+t)**alpha)-
           lambda**(x**alpha))
	return(ret)
}


#Generalized power Weibull integrated hazard rate function

igpw=function(x,t=1,alpha=1,theta=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | theta<=0,
           NaN,(1+(x+t)**alpha)**theta-
           (1+x**alpha)**theta)
	return(ret)
}


#Flexible Weibull integrated hazard rate function

ifw=function(x,t=1,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | alpha<=0 | beta<=0,
           NaN,exp(alpha*(x+t)-beta/(x+t))-
           exp(alpha*x-beta/x))
	return(ret)
}



#Generalized $F$ integrated hazard rate function

igenF=function(x,t=1,beta=0,sigma=1,m1=1,m2=1)
{
    ret	= ifelse(x<=0 | t<=0 | length(x)!=length(t)
           | sigma<=0 | m1<=0 | m2<=0,
           NaN,log((1-pbeta(m1*(exp(-beta)*x)**(1/sigma)/(m2+m1*(exp(-beta)*x)**(1/sigma)),shape1=m1,shape2=m2))/
           (1-pbeta(m1*(exp(-beta)*(x+t))**(1/sigma)/(m2+m1*(exp(-beta)*(x+t))**(1/sigma)),shape1=m1,shape2=m2))))
	return(ret)
}

#The function {\sf pbeta} is  from the {\sf R} base package.




#Gompertz quantile function

qgompertz=function(x,u=0.5,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0 | beta<=0,
           NaN, (1/beta)*
           log(1-(beta/alpha)*exp(-beta*x)*log(u)))
	return(ret)
}



#Perks quantile function

qperks=function(x,u=0.5,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0 | beta<=0,
           NaN, (1/beta)*
           (log((u**(-beta))*
           (1+exp(alpha+beta*x))-1)-alpha)-x)
	return(ret)
}



#Beard quantile function

qbeard=function(x,u=0.5,alpha=1,beta=1,rho=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0 | beta<=0 | rho<=0,
           NaN, (1/beta)*
           (log((u**(-beta*rho))*
           (1+alpha*rho*exp(beta*x))-1)-log(alpha)-log(rho))-x)
	return(ret)
}



#Exponential quantile function

qexponential=function(x,u=0.5,alpha=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0,
           NaN,-log(u)/alpha)
	return(ret)
}



#Pareto quantile function

qpareto=function(x,u=0.5,alpha=1,m=1)
{
	ret	= ifelse(x<=m | u<=0 | u>=1 | m<=0 | length(x)!=length(u) | alpha<=0,
           NaN,x*exp(-log(u)/alpha)-x)
	return(ret)
}



#Weibull quantile function

qweibull=function(x,u=0.5,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0 | sigma<=0,
           NaN, (x**sigma-alpha**sigma*log(u))**(1/sigma)-x)
	return(ret)
}



#Logistic quantile function

qlogistic=function(x,u=0.5,alpha=1,sigma=1)
{
	ret	= ifelse(u<=0 | u>=1 | length(x)!=length(u) | sigma<=0,
           NaN, sigma*
           (log(1+exp((x-alpha)/sigma)-u)-log(u))-x+alpha)
	return(ret)
}


#Log-logistic quantile function

qloglogis=function(x,u=0.5,alpha=1,sigma=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0 | sigma<=0,
           NaN, exp((1/sigma)*
           (log((1/u)*(1+alpha*x**sigma)-1)-log(alpha))-x))
	return(ret)
}



#Normal quantile function

qnormal=function(x,u=0.5,alpha=1,sigma=1)
{
	ret	= ifelse(u<=0 | u>=1 | length(x)!=length(u) | sigma<=0,
           NaN, sigma*
           qnorm(1-u*(1-pnorm((x-alpha)/sigma)))+x*alpha)
	return(ret)
}

#The functions {\sf pnorm} and {\sf qnorm} are  from the {\sf R} base package.




#Lognormal quantile function

qlognormal=function(x,u=0.5,alpha=1,sigma=1)
{
	ret=NaN
    if (x==0 & u>0 & u<1 & length(x)==length(u) & sigma>0)
        ret=exp(sigma*qnorm(u)+alpha)
    if (x>0 & u>0 & u<1 & length(x)==length(u) & sigma>0)
       ret=exp(sigma*qnorm(1-u*
              (1-pnorm((log(x)-alpha)/sigma)))+alpha)
	return(ret)
}

#The functions {\sf pnorm} and {\sf qnorm} are  from the {\sf R} base package.


#Inverse-Gaussian quantile function

qinversegaussian=function(x,u=0.5,alpha=1,sigma=1)
{
	m=length(x)
        ret=rep(NaN,m)
        if (x>0&u>0&u<1&length(x)==length(u)&alpha>0&sigma>0)
        {ret=x
        for (i in 1:m)
        {ff=function (t)
        {tt=pnorm(sqrt(sigma/x[i])*(x[i]/alpha-1))+exp(2*sigma/alpha)*pnorm(-sqrt(sigma/x[i])*(x[i]/alpha+1))
        tt2=pnorm(sqrt(sigma/(x[i]+t))*((x[i]+t)/alpha-1))+exp(2*sigma/alpha)*pnorm(-sqrt(sigma/(x[i]+t))*((x[i]+t)/alpha+1))
        return(log((1-tt)/(1-tt2))+log(u[i]))}
        ret[i]=uniroot(ff,lower=0,upper=1000)$root}}
	return(ret)
}

#The function {\sf pnorm} is from the {\sf R} base package.



#Gamma quantile function

qgammad=function(x,u=0.5,alpha=1,lambda=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | alpha<=0 | lambda<=0,
           NaN,qgamma(1-u*(1-pgamma(x,shape=lambda,scale=alpha)),shape=lambda,scale=alpha)-x)
	return(ret)
}

#The functions {\sf pgamma} and {\sf qgamma} are  from the {\sf R} base package.


#Generalized gamma quantile function

qgengammad=function(x,u=0.5,b=1,d=1,k=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | b<=0 | d<=0 | k<=0,
           NaN,b*(qgamma(1-u*(1-pgamma((x/b)**d,shape=k)),shape=k))**(1/d)-x)
	return(ret)
}

#The functions {\sf pgamma} and {\sf qgamma} are  from the {\sf R} base package.

#Linear quantile function

qlinear=function(x,u=0.5,a=1,b=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | a<0 | b<0 | a==0&b==0,
           NaN, (1/b)*(-(a+b*x)+
           sqrt(a*a+b*b*x*x+2*a*b*x+2*b*log(u))))
	return(ret)
}




#Uniform quantile function

quniform=function(x,u=0.5,a=1,b=2)
{
	ret	= ifelse(x<=a | x>=b | u<=0 | u>=1 | length(x)!=length(u) | b<=a | a<=0,
           NaN,(b-x)*(1-u))
	return(ret)
}



#Kumaraswamy quantile function

qkum=function(x,u=0.5,a=1,b=1)
{
	ret	= ifelse(x<=0 | x>=1 | u<=0 | u>=1 |
           length(x)!=length(u) | a<=0 | b<=0,
           NaN,(1-u**(-1/b)*
           (1-x**a))**(1/a)-x)
	return(ret)
}



#Gumbel II quantile function

qfrechet=function(x,u=0.5,a=1,b=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 |
           length(x)!=length(u) | a<=0 | b<=0,NaN,
           (x**{-a-1}+log(u)/b)**(-1/(a+1))-x)
	return(ret)
}




#Hjorth quantile function

qhjorth=function(x,u=0.5,delta=1,theta=1,beta=1)
{
	m=length(x)
    ret=rep(NaN,m)
    if (x>0&u>0&u<1&length(x)==length(u)&delta>0&theta>0&beta>0)
       {for (i in 1:m)
            {ff=function (t) {delta*x[i]*t+delta*t*t/2+
                     (theta/beta)*log(1+beta*t
                     /(1+beta*x[i]))+log(u[i])}
             ret[i]=uniroot(ff,lower=0,upper=100)$root}
       }
	return(ret)
}

#The function {\sf uniroot} is  from the {\sf R} base package.



#Additive Weibull quantile function

qaddweibull=function(x,u=0.5,a=1,b=1,c=1,d=1)
{
	m=length(x)
    ret=rep(NaN,m)
    if (x>0&u>0&u<1&length(x)==length(u)&a>0&b>0&c>0&d>0)
       {for (i in 1:m)
            {ff=function (t) {a**b*(x[i]+t)**b+
                     c**d*(x[i]+t)**d+log(u[i])}
             ret[i]=uniroot(ff,lower=0,upper=100)$root}
       }
	return(ret)
}

#The function {\sf uniroot} is  from the {\sf R} base package.


#Schabe quantile function

qschabe=function(x,u=0.5,theta=1,gamma=0.5)
{
	ret	= ifelse(x>theta | u<=0 | u>=1 | length(x)!=length(u)
           | theta<=0 | gamma<=0 | gamma>=1,NaN,
           theta-x-theta*(gamma+1)*
           (1-(theta*x)/(u*(theta-x))))
	return(ret)
}


#Lai quantile function

qlai=function(x,u=0.5,lambda=1,beta=1,nu=1)
{
	m=length(x)
    ret=rep(NaN,m)
    if (x>0&u>0&u<1&length(x)==length(u)&lambda>0&beta>=0&nu>=0)
       {for (i in 1:m)
            {ff=function (t) {lambda*(-x[i]**beta*
             genhypergeo(U=beta,L=1+beta,z=nu*x[i])
             +(x[i]+t)**beta*
             genhypergeo(U=beta,L=1+beta,z=nu*(x[i]+t))
             -(nu/(beta+1))*x[i]**(beta+1)*
             genhypergeo(U=1+beta,L=2+beta,z=nu*x[i])
             +(nu/(beta+1))*(x[i]+t)**(beta+1)*
             genhypergeo(U=1+beta,L=2+beta,z=nu*(x[i]+t)))}
             ret[i]=uniroot(ff,lower=0,upper=100)$root}
       }
	return(ret)
}

#The function {\sf uniroot} is  from the {\sf R} base package.
#The function {\sf genhypergeo} is  from the {\sf R} contributed package {\sf hypergeo}.



#Xie quantile function

qxie=function(x,u=0.5,lambda=1,alpha=1,beta=1)
{
	ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | lambda<=0 | alpha<=0 | beta<=0,NaN,
           alpha*(log(exp((x/alpha)**beta)-
           log(u)/(lambda*alpha)))**(1/beta)-x)
	return(ret)
}




#$J$-shaped quantile function

qjshape=function(x,u=0.5,b=1,nu=1)
{
	y=1-x/b
    ret	= ifelse(y<=0 | y>=1 | u<=0 | u>=1 | length(x)!=length(u)
           | b<=0 | nu<=0,NaN,b*(1-(1-(1-u*(1-(1-y*y)**nu)
           )**(1/nu))**(1/2))-x)
	return(ret)
}




#Beta quantile function

qbetad=function(x,u=0.5,a=1,b=1)
{
    ret	= ifelse(x<=0 | x>=1 | u<=0 | u>=1 | length(x)!=length(u)
           | a<=0 | b<=0,
           NaN,qbeta(1-u*(1-pbeta(x,
           shape1=a,shape2=b)),
           shape1=a,shape2=b)-x)
	return(ret)
}

#The functions  {\sf pbeta} and {\sf qbeta} are  from the {\sf R} base package.



#Exponentiated exponential quantile function

qee=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,
           NaN,qgen.exp(1-u*(1-pgen.exp(x,
           alpha=alpha,lambda=lambda)),
           alpha=alpha,lambda=lambda)-x)
	return(ret)
}

#The functions {\sf pgen.exp} and {\sf qgen.exp} are  from the {\sf R} contributed package {\sf reliaR}.



#Inverse generalized  exponential quantile function

qige=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,
           NaN,qinv.genexp(1-u*(1-pinv.genexp(x,
           alpha=alpha,lambda=lambda)),
           alpha=alpha,lambda=lambda)-x)
	return(ret)
}

#The functions {\sf pinv.genexp} and {\sf qinv.genexp} are  from the {\sf R} contributed package {\sf reliaR}.


#Exponentiated Weibull quantile function

qew=function(x,u=0.5,alpha=1,c=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | c<=0 | lambda<=0,NaN,
           (1/lambda)*qexpo.weibull(1-u*
           (1-pexpo.weibull(lambda*x,
           alpha=c,theta=alpha)),
           alpha=c,theta=alpha)-x)
	return(ret)
}

#The functions {\sf pexpo.weibull} and {\sf qpexpo.weibull} are  from the {\sf R} contributed package {\sf reliaR}.

#Exponentiated logistic quantile function

qel=function(x,u=0.5,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | beta<=0,NaN,qexpo.logistic(1-u*
           (1-pexpo.logistic(x,
           alpha=alpha,beta=beta)),
           alpha=alpha,beta=beta)-x)
	return(ret)
}

#The functions {\sf pexpo.logistic} and {\sf qexpo.logistic} are  from the {\sf R} contributed package {\sf reliaR}.


#BurrX quantile function

qburrx=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,NaN,qburrX(1-u*
           (1-pburrX(x,
           alpha=alpha,lambda=lambda)),
           alpha=alpha,lambda=lambda)-x)
	return(ret)
}

#The functions {\sf pburrX} and {\sf qburrX} are  from the {\sf R} contributed package {\sf reliaR}.


#Gumbel quantile function

qgumbeld=function(x,u=0.5,mu=1,sigma=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u) | sigma<=0,
           NaN,qgumbel(1-u*(1-pgumbel(x,
           mu=mu,sigma=sigma)),
           mu=mu,sigma=sigma)-x)
	return(ret)
}

#The functions {\sf pgumbel} and {\sf qgumbel} are  from the {\sf R} contributed package {\sf reliaR}.



#Exponential extension quantile function

qexpext=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,NaN,
           (1/lambda)*(((1+lambda*x)**alpha-
           log(u))**(1/alpha)-1-lambda*x))
	return(ret)
}




#Chen quantile function

qchen=function(x,u=0.5,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | beta<=0 | lambda<=0,NaN,
           (log(exp(x**beta)-
           log(u)/lambda))**(1/beta)-x)
	return(ret)
}




#Loggamma quantile function

qlgammad=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=1 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,
           NaN,qlgamma(1-u*(1-plgamma(x,shapelog=alpha,
           ratelog=lambda)),shapelog=alpha,
           ratelog=lambda)-x)
	return(ret)
}

#The functions {\sf plgamma} and {\sf qlgamma} are  from the {\sf R} contributed package {\sf actuar}.



#Marshall-Olkin exponential quantile function

qmoe=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,NaN,
           (1/lambda)*log(1-alpha+(1/u)*
           (exp(lambda*x)-1+alpha))-x)
	return(ret)
}




#Marshall-Olkin Weibull quantile function

qmow=function(x,u=0.5,alpha=1,beta=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | beta<=0 | lambda<=0,NaN,
           (1/lambda)*(log(1-alpha+(1/u)*
           (exp((lambda*x)**beta)-
           1+alpha)))**(1/beta)-x)
	return(ret)
}




#Logistic exponential quantile function

qle=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,
           NaN,qlogis.exp(1-u*
           (1-plogis.exp(x,
           alpha=alpha,lambda=lambda)),
           alpha=alpha,lambda=lambda)-x)
	return(ret)
}

#The functions {\sf plogis.exp} and {\sf qlogis.exp} are  from the {\sf R} contributed package {\sf reliaR}.




#Logistic Rayleigh quantile function

qlr=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,
           NaN,qlogis.rayleigh(1-u*
           (1-plogis.rayleigh(x,
           alpha=alpha,lambda=lambda)),
           alpha=alpha,lambda=lambda)-x)
	return(ret)
}

#The functions {\sf plogis.rayleigh} and {\sf qlogis.rayleigh} are  from the {\sf R} contributed package {\sf reliaR}.



#Loglog quantile function

qll=function(x,u=0.5,alpha=1,lambda=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | lambda<=0,NaN,
           ((-log(u)+lambda**(x**alpha))/
           (log(lambda)))**(1/alpha)-x)
	return(ret)
}




#Generalized power Weibull quantile function

qgpw=function(x,u=0.5,alpha=1,theta=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | theta<=0,NaN,
           (((1+x**alpha)**theta-
           log(u))**(1/theta)-1)**
           (1/alpha)-x)
	return(ret)
}




#Flexible Weibull quantile function

qfw=function(x,u=0.5,alpha=1,beta=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | alpha<=0 | beta<=0,NaN,
           (1/(2*alpha))*(log(-log(u)+
           exp(alpha*x-beta/x))+
           sqrt((log(-log(u)+
           exp(alpha*x-beta/x)))**2+
           4*alpha*beta))-x)
	return(ret)
}



#Generalized $F$ quantile function

qgenF=function(x,u=0.5,beta=0,sigma=1,m1=1,m2=1)
{
    ret	= ifelse(x<=0 | u<=0 | u>=1 | length(x)!=length(u)
           | sigma<=0 | m1<=0 | m2<=0,
           NaN,exp(beta)*m1**(-sigma)*(1/(1-qbeta(1-(1-pbeta(m1*(exp(-beta)*x)**(1/sigma)/
           (m2+m1*(exp(-beta)*x)**(1/sigma)),
           shape1=m1,shape2=m2))*u,shape1=m1,shape2=m2))-m2)**sigma-x)
	return(ret)
}

#The functions {\sf pbeta} and {\sf qbeta} are  from the {\sf R} base package.

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