Generalized half-logistic Poisson distributions

Abstract

In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the r th moment, moment generating function, Shannon entropy and Rényi entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

“…The data set is the remission times (in months) of a random sample of 128 bladder cancer patients provided by [39] also studied by [40], the data set are: The numerical value of the estimators, ℓ(Θ) and the KS are given in table 4. The result shows that KwEUq has the smallest value of KS thus, KwEUq fit the data better than the other models.…”

A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

“…Recently, the characterization of Lindley distribution based on conditional expectations was discussed by [33]. Here we are able to characterize the sub model of PoiGHL distribution (i.e if a = 1) known as the half logistic Poisson (HLP) [12] based on some certain functional conditional expectations. The probability density, cumulative distribution function of the HLP with…”

“…• Half logistic (HL) F(x) = 1−e −αx 1+e −αx , x, α > 0. The first data set is the remission times (in months) of a random sample of 128 bladder cancer patients provided by [48] also analyzed by [46] The second data set from [49] also studied by [2] it consist of the failure times of 20 mechanical components. The data are: 0.067, 0.068, 0.076, 0.081, 0.084, 0.085, 0.085, 0.086, 0.089, 0.098, 0.098, 0.114, 0.114, 0.115, 0.121, 0.125, 0.131, 0.149, 0.160, 0.485.…”

“…It can be seen that this technique allow us to propose more realistic statistical models that extend the well-known classical models and at the same time provide great flexibility in a variety of applications. The reader is referred to the following for an overview of the compound of discrete and continuous distribution: the exponential geometric (EG) [3], Poisson-exponential (PE) [4], generalized exponential-power series (GEPS) [5], linear failure rate-power series (LFPS) [6], exponentiated Weibull-Poisson (EWP) [7], exponentiated Weibull-logarithmic (EWL) [8], exponentiated Weibull power series (EWP) [9], complementary exponentiated BurrXII Poisson (CEBXIIP) [10], Poisson-odd generalized exponential (POGE) [11], half logistic Poisson (HLP) [12], Poison half logistic (PHL) [13] among others.…”

Characterization of Marshall-Olkin-G family of distributions by truncated moments

“…[1] provide a characterization of Lindley distribution (L) based on left and right truncated moments. [14] characterized half logistic Poisson distribution (HLP) [15] based on left and right truncated moments. [10] characterized Lindley distribution (L) based on truncated moments of order statistics.…”