| zih.mle {AZIAD} | R Documentation |
Maximum likelihood estimate for Zero-Inflated or Zero-Altered discrete and continuous distributions.
Description
Calculate the Maximum likelihood estimate and the corresponding negative log likelihood value for Zero-Inflated or Zero-Altered 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
zih.mle(x,r,p,alpha1,alpha2,n,lambda,mean,sigma,
type=c("zi","h"),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 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 postive 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. |
type |
the type of distribution used to calculate the sample estimate, where 'zi' stand for zero-inflated and 'h' stands for hurdle distributions. |
dist |
The distribution used to calculate the maximum likelihood estimate. Can be one of 'poisson.zihmle', 'geometric.zihmle', 'nb.zihmle', 'nb1.zihmle', 'bb.zihmle', 'bb1.zihmle', 'bnb.zihmle', 'bnb1.zihmle', 'normal.zihmle', 'halfnorm.zihmle', 'lognorm.zimle', 'exp.zihmle', which corresponds to Zero-Inflated or Zero-Hurdle Poisson, geometric, negative binomial, negative binomial1, beta binomial, beta binomial1, beta negative binomial, beta negative binomial1, normal, log normal, half 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
zih.mle calculate the Maximum likelihood estimate and the corresponding negative log likelihood of Zero-Inflated or Zero-Hurdle Poisson, geometric, negative binomial, negative binomial1, beta binomial, beta binomial1, beta negative binomial, beta negative binomial1, normal, log normal, half normal, and exponential distributions.
If dist = poisson.zihmle, the following values are returned:
lambda: the maximum likelihood estimate of
\lambda.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimate plugged-in.
If dist = geometric.zihmle, the following values are returned:
p: the maximum likelihood estimate of p.
phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimate plugged-in.
If dist = nb.zihmle, the following values are returned:
r: the maximum likelihood estimate of r.
p: the maximum likelihood estimate of p.
phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = nb1.zihmle, the following values are returned:
r: the maximum likelihood estimate of rounded r (returns integer estimate).
p: the maximum likelihood estimate of p.
phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bb.zihmle, the following values are returned:
n: the maximum likelihood estimate of n.
alpha1: the maximum likelihood estimate of
\alpha_1.alpha2: the maximum likelihood estimate of
\alpha_2.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bb1.zihmle, the following values are returned:
n: the maximum likelihood estimate of rounded n (returns integer estimate).
alpha1: the maximum likelihood estimate of
\alpha_1.alpha2: the maximum likelihood estimate of
\alpha_2.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bnb.zihmle, the following values are returned:
r: the maximum likelihood estimate of r.
alpha1: the maximum likelihood estimate of
\alpha_1.alpha2: the maximum likelihood estimate of
\alpha_2.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = bnb1.zihmle, the following values are returned:
r: the maximum likelihood estimate of rounded r (returns integer estimate).
alpha1: the maximum likelihood estimate of
\alpha_1.alpha2: the maximum likelihood estimate of
\alpha_2.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = normal.zihmle, the following values are returned:
mean: the maximum likelihood estimate of
\mu.sigma: the maximum likelihood estimate of
\sigma.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = lognorm.zihmle, the following values are returned:
mean: the maximum likelihood estimate of
\mu.sigma: the maximum likelihood estimate of
\sigma.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = halfnorm.zihmle, the following values are returned:
sigma: the maximum likelihood estimate of
\sigma.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
If dist = exp.zihmle, the following values are returned:
lambda: the maximum likelihood estimate of
\lambda.phi: the maximum likelihood estimate of
\phi.loglik: the value of negative log likelihood with maximum likelihood estimates plugged-in.
Value
A row vector containing the maximum likelihood estimate of the unknown parameters and the corresponding value of negative log likelihood.
References
H. Aldirawi, J. Yang (2019). Model Selection and Regression Analysis for Zero-altered or Zero-inflated Data, Statistical Laboratory Technical Report, no.2019-01, University of Illinois at Chicago.
Examples
set.seed(007)
x1=sample.zi1(2000,phi=0.3,dist='poisson',lambda=2)
zih.mle(x1,lambda=10,dist="poisson.zihmle",type="zi")
#2.00341 0.3099267 -3164.528
x2=sample.zi1(2000,phi=0.3,dist='geometric',p=0.2)
zih.mle(x2,p=0.3,dist="geometric.zihmle",type="zi")
#0.1976744 0.2795942 -4269.259
x3=sample.zi1(2000,phi=0.3,dist='nb',r=10,p=0.3)
zih.mle(x3,r=2,p=0.2,dist="nb.zihmle",type="zi")
#10.18374 0.3033975 0.2919962 -6243.002
zih.mle(x3,r=2,p=0.2,dist="nb1.zihmle",type="zi")
#10 0.2995633 0.2919959 -6243.059
x4=sample.zi1(2000,phi=0.3,dist='bb',n=10,alpha1=2,alpha2=4)
zih.mle(x4,n=10,alpha1=3,alpha2=4,dist="bb.zihmle",type="zi")
#9.99 1.862798 3.756632 0.2643813 -3982.646
zih.mle(x4,n=10,alpha1=3,alpha2=4,dist="bb1.zihmle",type="zi")
#10 1.866493 3.76888 0.2644992 -3982.682
x5=sample.zi1(2000,phi=0.3,dist='bnb',r=5,alpha=3,alpha2=3)
zih.mle(x5,r=10,alpha1=3,alpha2=4,dist="bnb.zihmle",type="zi")
#6.936502 3.346791 2.32905 0.285682 -5088.173
zih.mle(x5,r=10,alpha1=3,alpha2=4,dist="bnb1.zihmle",type="zi")
#7 3.353377 2.313633 0.2855203 -5088.173
x6=sample.zi1(2000,phi=0.3,dist="normal",mean=10,sigma=2)
zih.mle(x6,mean=2,sigma=2,dist="normal.zihmle",type="zi")
#9.988447 2.015987 0.28 -4242.18
x7=sample.zi1(2000,phi=0.3,dist="lognormal",mean=1,sigma=4)
zih.mle(x7,mean=4,sigma=2,dist="lognorm.zihmle",type="zi")
#1.003887 3.945388 0.2985 -6544.087
x8=sample.zi1(2000,phi=0.3,dist="halfnormal",sigma=4)
zih.mle(x8,sigma=1,dist="halfnorm.zihmle",type="zi")
#1.292081 0.294 -8573.562
x9=sample.zi1(2000,phi=0.3,dist="exponential",lambda=20)
zih.mle(x9,lambda=10,dist="exp.zihmle",type="zi")
#20.1165 0.294 1614.786
set.seed(008)
y1=sample.h1(2000,phi=0.3,dist='poisson',lambda=10)
zih.mle(y1,lambda=10,dist="poisson.zihmle",type="h")
#10.11842 0.3015 -4826.566
y2=sample.h1(2000,phi=0.3,dist='geometric',p=0.3)
zih.mle(y2,p=0.2,dist="geometric.zihmle",type="h")
#0.3050884 0.2925 -4061.65
y3=sample.h1(2000,phi=0.3,dist='nb',r=10,p=0.3)
zih.mle(y3,r=2,p=0.2,dist="nb.zihmle",type="h")
#9.50756 0.2862545 0.297 -6261.479
zih.mle(y3,r=2,p=0.2,dist="nb1.zihmle",type="h")
#10 0.2966819 0.297 -6261.932
y4=sample.h1(2000,phi=0.3,dist='bb',n=10,alpha1=2,alpha2=4)
zih.mle(y4,n=10,alpha1=3,alpha2=4,dist="bb.zihmle",type="h")
#9.99 1.894627 3.851142 0.293 -4092.983
zih.mle(y4,n=10,alpha1=3,alpha2=4,dist="bb1.zihmle",type="h")
#10 1.898415 3.863768 0.293 -4093.004
y5=sample.h1(2000,phi=0.3,dist='bnb',r=5,alpha=3,alpha2=3)
zih.mle(y5,r=10,alpha1=3,alpha2=4,dist="bnb.zihmle",type="h")
#3.875685 3.026982 3.874642 0.328 -5274.091
zih.mle(y5,r=10,alpha1=3,alpha2=4,dist="bnb1.zihmle",type="h")
#4 3.028185 3.756225 0.328 -5274.092
y6=sample.h1(2000,phi=0.3,dist="normal",mean=10,sigma=2)
zih.mle(y6,mean=2,sigma=2,dist="normal.zihmle",type="h")
#10.01252 1.996997 0.29 -4201.334
y7=sample.h1(2000,phi=0.3,dist="lognormal",mean=1,sigma=4)
zih.mle(y7,mean=4,sigma=2,dist="lognorm.zihmle",type="h")
#0.9305549 3.891624 0.287 -6486.92
y8=sample.h1(2000,phi=0.3,dist="halfnormal",sigma=4)
zih.mle(y8,sigma=1,dist="halfnorm.zihmle",type="h")
#1.26807 0.3 -8863.063
y9=sample.h1(2000,phi=0.3,dist="exponential",lambda=20)
zih.mle(y9,lambda=10,dist="exp.zihmle",type="h")
#20.26938 0.2905 1645.731