FI.ZI | R Documentation |
Computes the inverse of the fisher information matrix for Poisson, geometric, negative binomial, beta binomial, beta negative binomial, normal, lognormal, half normal, and exponential distributions and their zero-inflated and hurdle versions along with the confidence intervals of all parameters in the model.
FI.ZI(x,dist="poisson",r=NULL,p=NULL,alpha1=NULL,alpha2=NULL, n=NULL,lambda=NULL,mean=NULL,sigma=NULL,lowerbound=0.01,upperbound=10000)
x |
A vector of count data. Should be non-negative integers for discrete cases. Random generation for continuous cases. |
dist |
The distribution used to calculate the inverse of fisher information and confidence interval. It can be one of 'poisson','geometric','nb','bb','bnb','normal','halfnormal','lognormal','exponential', 'zip','zigeom','zinb','zibb','zibnb', 'zinormal','zilognorm','zohalfnorm','ziexp', 'ph','geomh','nbh','bbh','bnbh' which corresponds to general Poisson, geometric, negative binomial, beta binomial, beta negative binomial, normal, log normal, half normal, exponential, Zero-Inflated Poisson, Zero-Inflated geometric, Zero-Inflated negative binomial, Zero-Inflated beta binomial, Zero-Inflated beta negative binomial, Zero-Inflated/hurdle normal, Zero-Inflated/hurdle log normal, Zero-Inflated/hurdle half normal, Zero-Inflated/hurdle exponential, Zero-Hurdle Poisson, Zero-Hurdle geometric, Zero-Hurdle negative binomial, Zero-Hurdle beta binomial, and Zero-Hurdle beta negative binomial distributions, respectively. |
r |
An initial value of the number of success before which m failures are observed, where m is the element of x. Must be a positive number, but not required to be an integer. |
p |
An initial value of the probability of success, should be a positive value within (0,1). |
alpha1 |
An initial value for the first shape parameter of beta distribution. Should be a positive number. |
alpha2 |
An initial value for the second shape parameter of beta distribution. Should be a positive number. |
n |
An initial value of the number of trials. Must be a positive number, but not required to be an integer. |
lambda |
An initial value of the rate. Must be a positive real number. |
mean |
An initial value of the mean or expectation. |
sigma |
An initial value of the standard deviation. Must be a positive real number. |
lowerbound |
A lower searching bound used in the optimization of likelihood function. Should be a small positive number. The default is 1e-2. |
upperbound |
An upper searching bound used in the optimization of likelihood function. Should be a large positive number. The default is 1e4. |
FI.ZI calculate the inverse of the fisher information matrix and the corresponding confidence interval of the parameter of general, Zero-Inflated, and Zero-Hurdle Poisson, geometric, negative binomial, beta binomial, beta negative binomial, normal, log normal, half normal, and exponential distributions. Note that zero-inflated and hurdle are the same in continuous distributions.
A list containing the inverse of the fisher information matrix and the corresponding 95% confidence interval for all the parameters in the model.
Aldirawi H, Yang J (2022). “Modeling Sparse Data Using MLE with Applications to Micro- biome Data.” Journal of Statistical Theory and Practice, 16(1), 1–16.
set.seed(111) N=1000;lambda=10; x<-stats::rpois(N,lambda=lambda) FI.ZI(x,lambda=5,dist="poisson") #$inversefisher # lambda #[1,] 9.896 #$ConfidenceIntervals #[1] 9.701025 10.090974 set.seed(111) N=1000;lambda=10;phi=0.4; x1<-sample.h1(N,lambda=lambda,phi=phi,dist="poisson") FI.ZI(x1,lambda=4,dist="ph") #$inversefisher # [,1] [,2] #[1,] 0.237679 0.00000 #[2,] 0.000000 16.12686 #$ConfidenceIntervals # [,1] [,2] #CI of Phi 0.3587835 0.4192165 #CI of lambda 9.6000082 10.0978060 set.seed(289) N=2000;mean=10;sigma=2;phi=0.4; x<-sample.zi1(N,phi=phi,mean=mean,sigma=sigma,dist="lognormal") FI.ZI(x, mean=1,sigma=1, dist="zilognorm") # $inversefisher # [,1] [,2] [,3] #[1,] 0.6313214 0.000000 0.000000 #[2,] 0.0000000 6.698431 0.000000 #[3,] 0.0000000 0.000000 3.349215 #$ConfidenceIntervals # [,1] [,2] #CI of phi 0.3521776 0.4218224 #CI of mean 9.8860358 10.1128915 #CI of sigma 1.9461552 2.1065664
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