AZIAD (version 0.0.3)

FI.ZI: Inverse Fisher Information matrix and confidence intervals of the parameters for general, continuous, and discrete zero-inflated or hurdle distributions.

Description

Computes the inverse of the fisher information matrix for Poisson, geometric, negative binomial, beta binomia, 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.

Usage

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)

Value

A list containing the inverse of the fisher information matrix and the corresponding 95% confidence interval for all the parameters in the model.

Arguments

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.

Details

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.

References

• 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.

Examples

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