new.mle: Maximum likelihood estimate for general discrete and...
In AZIAD: Analyzing Zero-Inflated and Zero-Altered Data
new.mle R Documentation
Maximum likelihood estimate for general discrete and continuous distributions
Description
calculate the Maximum likelihood estimate and the corresponding negative log likelihood value for
general Poisson, geometric, negative binomial, negative binomial1,
beta binomial, beta binomial1, beta negative binomial, beta negative binomial1,
normal, half normal, log normal, and exponential distributions.
Usage
new.mle(x,r,p,alpha1,alpha2,n,lambda,mean,sigma,dist,lowerbound=0.01,upperbound=10000)
Arguments
x
A vector of count data which should non-negative integers for discrete cases. Real valued random generation for continuous cases.
r
An initial value for 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 for 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 for the number of trials. Must be a positive number, but not required to be an integer.
lambda
An initial value for the rate. Must be a positive real number.
mean
An initial value of the mean or expectation. A real number
sigma
An initial value of the standard deviation. Must be a positive real number.
dist
The distribution used to calculate the maximum likelihood estimate. Can
be one of 'poisson', 'geometric', 'nb', 'nb1', 'bb', 'bb1', 'bnb', 'bnb1', 'normal', 'halfnormal',
'lognormal', 'exponential', which corresponds to Poisson, geometric, negative binomial, negative binomial1,
beta binomial, beta binomial1, beta negative binomial, beta negative binomial1,
normal, half normal, log normal, and exponential distributions.
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.
Details
new.mle calculate Maximum likelihood estimate and corresponding negative log likelihood
of general Poisson, geometric, negative binomial, negative binomial1,
beta binomial, beta binomial1, beta negative binomial, beta negative binomial1,
normal, half normal, log normal, and exponential distributions.
Value
A row vector containing the maximum likelihood estimate of the unknown parameters and the corresponding value of negative log likelihood.
If dist = poisson, the following values are returned:
lambda: the maximum likelihood estimate of λ.
loglik: the value of negative log likelihood with maximum likelihood estimate plugged-in.
If dist = geometric, the following values are returned:
p: the maximum likelihood estimate of p.
loglik: the value of negative log likelihood with maximum likelihood estimate plugged-in.
If dist = nb, the following values are returned:
r: the maximum likelihood estimate of r.
p: the maximum likelihood estimate of p.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = nb1, the following values are returned:
r: the maximum likelihood estimate of rounded r (returns integer estimate).
p: the maximum likelihood estimate of p.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bb, the following values are returned:
n: the maximum likelihood estimate of n.
alpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bb1, the following values are returned:
n: the maximum likelihood estimate of rounded n (returns integer estimate).
alpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bnb, the following values are returned:
r: the maximum likelihood estimate of r.
a lpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bnb1, the following values are returned:
r: the maximum likelihood estimate of rounded r (returns integer estimate).
alpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = normal, the following values are returned:
mean: the maximum likelihood estimate of μ.
sigma: the maximum likelihood estimate of σ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = lognormal, the following values are returned:
mean: the maximum likelihood estimate of μ.
sigma: the maximum likelihood estimate of σ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = halfnormal, the following values are returned:
sigma: the maximum likelihood estimate of σ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = exponential, the following values are returned:
lambda: the maximum likelihood estimate of λ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
References
H. Aldirawi, J. Yang, A. A. Metwally (2019). Identifying Appropriate Probabilistic Models for Sparse Discrete Omics Data, accepted for publication in 2019 IEEE EMBS International Conference on Biomedical & Health Informatics (BHI).
Examples
set.seed(001)
x1=stats::rpois(1000,lambda=10)
new.mle(x1,lambda=3,dist="poisson") #9.776 -2611.242
x2=stats::rgeom(1000,prob=0.2)
new.mle(x2,p=0.5,dist="geometric") #0.1963865 -2522.333
x3=stats::rnbinom(1000,size=5,prob=0.3)
new.mle(x3,r=2,p=0.6,dist="nb") #5.113298 0.3004412 -3186.163
new.mle(x3,r=2,p=0.6,dist="nb1") #5 0.299904 -3202.223
x4=extraDistr::rbbinom(1000,size=4,alpha=2,beta=3)
new.mle(x4,n=10,alpha1=3,alpha2=4,dist="bb") #3.99 1.78774 2.680009 -1533.982
new.mle(x4,n=10,alpha1=3,alpha2=4,dist="bb1") #4 1.800849 2.711264 -1534.314
x5=extraDistr::rbnbinom(1000, size=5, alpha=3,beta=3)
new.mle(x5,r=5,alpha1=3,alpha2=4,dist="bnb") #5.472647 3.008349 2.692704 -3014.372
new.mle(x5,r=5,alpha1=3,alpha2=4,dist="bnb1") #5 2.962727 2.884826 -3014.379
x6=stats::rnorm(1000,mean=10,sd=2)
new.mle(x6,mean=2,sigma=1,dist="normal") #9.976704 2.068796 -2145.906
x7=stats::rlnorm(1000, meanlog = 1, sdlog = 4)
new.mle(x7,mean=2,sigma=2,dist="lognormal") #0.9681913 3.299503 -3076.156
x8=extraDistr::rhnorm(1000, sigma = 3)
new.mle(x8,sigma=2,dist="halfnormal") #3.103392 -1858.287
x9=stats::rexp(1000,rate=1.5)
new.mle(x9,lambda=3,dist="exponential") #1.454471 -625.3576
AZIAD documentation built on Aug. 14, 2022, 9:05 a.m.
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| new.mle | R Documentation |
Maximum likelihood estimate for general discrete and continuous distributions
Description
calculate the Maximum likelihood estimate and the corresponding negative log likelihood value for general Poisson, geometric, negative binomial, negative binomial1, beta binomial, beta binomial1, beta negative binomial, beta negative binomial1, normal, half normal, log normal, and exponential distributions.
Usage
new.mle(x,r,p,alpha1,alpha2,n,lambda,mean,sigma,dist,lowerbound=0.01,upperbound=10000)
Arguments
x |
A vector of count data which should non-negative integers for discrete cases. Real valued random generation for continuous cases. |
r |
An initial value for 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 for 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 for the number of trials. Must be a positive number, but not required to be an integer. |
lambda |
An initial value for the rate. Must be a positive real number. |
mean |
An initial value of the mean or expectation. A real number |
sigma |
An initial value of the standard deviation. Must be a positive real number. |
dist |
The distribution used to calculate the maximum likelihood estimate. Can be one of 'poisson', 'geometric', 'nb', 'nb1', 'bb', 'bb1', 'bnb', 'bnb1', 'normal', 'halfnormal', 'lognormal', 'exponential', which corresponds to Poisson, geometric, negative binomial, negative binomial1, beta binomial, beta binomial1, beta negative binomial, beta negative binomial1, normal, half normal, log normal, and exponential distributions. |
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. |
Details
new.mle calculate Maximum likelihood estimate and corresponding negative log likelihood of general Poisson, geometric, negative binomial, negative binomial1, beta binomial, beta binomial1, beta negative binomial, beta negative binomial1, normal, half normal, log normal, and exponential distributions.
Value
A row vector containing the maximum likelihood estimate of the unknown parameters and the corresponding value of negative log likelihood.
If dist = poisson, the following values are returned:
lambda: the maximum likelihood estimate of λ.
loglik: the value of negative log likelihood with maximum likelihood estimate plugged-in.
If dist = geometric, the following values are returned:
p: the maximum likelihood estimate of p.
loglik: the value of negative log likelihood with maximum likelihood estimate plugged-in.
If dist = nb, the following values are returned:
r: the maximum likelihood estimate of r.
p: the maximum likelihood estimate of p.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = nb1, the following values are returned:
r: the maximum likelihood estimate of rounded r (returns integer estimate).
p: the maximum likelihood estimate of p.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bb, the following values are returned:
n: the maximum likelihood estimate of n.
alpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bb1, the following values are returned:
n: the maximum likelihood estimate of rounded n (returns integer estimate).
alpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bnb, the following values are returned:
r: the maximum likelihood estimate of r.
a lpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bnb1, the following values are returned:
r: the maximum likelihood estimate of rounded r (returns integer estimate).
alpha1: the maximum likelihood estimate of α_1.
alpha2: the maximum likelihood estimate of α_2.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = normal, the following values are returned:
mean: the maximum likelihood estimate of μ.
sigma: the maximum likelihood estimate of σ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = lognormal, the following values are returned:
mean: the maximum likelihood estimate of μ.
sigma: the maximum likelihood estimate of σ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = halfnormal, the following values are returned:
sigma: the maximum likelihood estimate of σ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = exponential, the following values are returned:
lambda: the maximum likelihood estimate of λ.
loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
References
H. Aldirawi, J. Yang, A. A. Metwally (2019). Identifying Appropriate Probabilistic Models for Sparse Discrete Omics Data, accepted for publication in 2019 IEEE EMBS International Conference on Biomedical & Health Informatics (BHI).
Examples
set.seed(001) x1=stats::rpois(1000,lambda=10) new.mle(x1,lambda=3,dist="poisson") #9.776 -2611.242 x2=stats::rgeom(1000,prob=0.2) new.mle(x2,p=0.5,dist="geometric") #0.1963865 -2522.333 x3=stats::rnbinom(1000,size=5,prob=0.3) new.mle(x3,r=2,p=0.6,dist="nb") #5.113298 0.3004412 -3186.163 new.mle(x3,r=2,p=0.6,dist="nb1") #5 0.299904 -3202.223 x4=extraDistr::rbbinom(1000,size=4,alpha=2,beta=3) new.mle(x4,n=10,alpha1=3,alpha2=4,dist="bb") #3.99 1.78774 2.680009 -1533.982 new.mle(x4,n=10,alpha1=3,alpha2=4,dist="bb1") #4 1.800849 2.711264 -1534.314 x5=extraDistr::rbnbinom(1000, size=5, alpha=3,beta=3) new.mle(x5,r=5,alpha1=3,alpha2=4,dist="bnb") #5.472647 3.008349 2.692704 -3014.372 new.mle(x5,r=5,alpha1=3,alpha2=4,dist="bnb1") #5 2.962727 2.884826 -3014.379 x6=stats::rnorm(1000,mean=10,sd=2) new.mle(x6,mean=2,sigma=1,dist="normal") #9.976704 2.068796 -2145.906 x7=stats::rlnorm(1000, meanlog = 1, sdlog = 4) new.mle(x7,mean=2,sigma=2,dist="lognormal") #0.9681913 3.299503 -3076.156 x8=extraDistr::rhnorm(1000, sigma = 3) new.mle(x8,sigma=2,dist="halfnormal") #3.103392 -1858.287 x9=stats::rexp(1000,rate=1.5) new.mle(x9,lambda=3,dist="exponential") #1.454471 -625.3576
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