MLE of continuous univariate distributions defined on the positive line {MLE}

MLE of continuous univariate distributions defined on the positive line

Description

MLE of continuous univariate distributions defined on the positive line.

Usage

positive.mle(x, distr = "gamma", tol = 1e-07, maxiters = 100)

Arguments

x

A vector with positive valued data (zeros are not allowed).

distr

The distribution to fit. "gamma" stands for the gamma distribution, "chisq" for the \chi^2 distribution, "weibull" for the Weibull, "lomax" for the Lomax, "foldnorm" for the folded normal, "betaprime" for the beta-prime distribution, "lognorm" for the log-normal, "logcauchy" for the log-Cauchy, "loglogictic" for the log-logistic distribution. "halfnorm" for the half-normal, "invgauss" for the inverse Gaussian, "pareto" for the Pareto distribution, "exp" for the exponential distribution, "exp2" I do not remember, "maxboltz" for the Maxwell-Boltzman distribution, "rayleigh" is the Rayleigh distribution, "lindley" is the Lindley distribution, "halfcauchy" is the half-Cauchy distribution and "powerlaw" is the power law distribution. The "normlog" is simply the normal distribution where all values are positive. Note, this is not log-normal. It is the normal with a log link. Similarly to the inverse gaussian distribution where the mean is an exponentiated. This comes from the GLM theory. The "epois" stands for the exponential-Poisson, the "gep" for the generalized exponential-Poisson and the "pe" for the Poisson-exponential distribution, the "zigamma" and "ziweibull" stand for the zero inflated gamma and Weibull distributions, respectively, and they accept zeros.

tol

The tolerance level up to which the maximisation stops; set to 1e-07 by default.

maxiters

The maximum number of iterations the Newton-Raphson will perform.

Details

Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. See wikipedia for the equations to be solved. For the t distribution we need the degrees of freedom and estimate the location and scatter parameters.

Value

Usually a list with three elements, but this is not for all cases.

iters

The number of iterations required for the Newton-Raphson to converge.

loglik

The value of the maximised log-likelihood.

param

The vector of the parameters.

Author(s)

Michail Tsagris and Sofia Piperaki.

R implementation and documentation: Michail Tsagris [e-mail] and Sofia Piperaki [e-mail].

References

Kalimuthu Krishnamoorthy, Meesook Lee and Wang Xiao (2015). Likelihood ratio tests for comparing several gamma distributions. Environmetrics, 26(8):571–583.

N.L. Johnson, S. Kotz and N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1 (2nd Edition).

N.L. Johnson, S. Kotz a nd N. Balakrishnan (1970). Distributions in statistics: continuous univariate distributions, Volume 2.

Tsagris M., Beneki C. and Hassani H. (2014). On the folded normal distribution. Mathematics, 2(1):12–28.

Sharma V. K., Singh S. K., Singh U. and Agiwal V. (2015). The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. Journal of Industrial and Production Engineering, 32(3): 162–173.

Barreto-Souza W. and Cribari-Neto F. (2009). A generalization of the exponential-Poisson distribution. Statistics and Probability Letters, 79(24): 2493–2500.

Louzada F., Ramos P. L. and Ferreira H. P. (2020). Exponential-Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence. Communications in Statistics–Simulation and Computation, 49(4): 1024–1043.

Rodrigues G. C., Louzada F. and Ramos P. L. (2018). Poisson-exponential distribution: different methods of estimation. Journal of Applied Statistics, 45(1): 128–144.

Taylor S. and Pollard K. (2009). Hypothesis Tests for Point-Mass Mixture Data with Application to Omics Data with Many Zero Values. Statistical Applications in Genetics and Molecular Biology, 8(1): 1–43.

You can also check the relevant wikipedia pages for these distributions.

See Also

disc.mle, real.mle, prop.mle

Examples

x <- rgamma(100, 3, 4)
positive.mle(x, distr = "gamma")