Poisson-odd generalized exponential family of distributions: Theory and Applications

Muhammad, Mustapha

doi:10.15672/hjms.2016.393

Cited by 15 publications

(14 citation statements)

References 39 publications

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“…Proposition 6. Let X be a random variable with pdf in (5), If Y = 1 γ log γ log 1+e −αx 2e −αx + θ /θ , then Y has the Poisson generalized Gompertz (PGG) with parameters a, θ, γ, λ > 0, mention in [11] and if a = 1 we have Gompertz Poisson (GP) [29]. therefore,…”

Section: Some Related Distributionsmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Muhammad

Liu

2019

Entropy

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In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of R = P ( X 1 < X 2 ) based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.

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Section: Some Related Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Muhammad

Liu

2019

Entropy

Self Cite

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“…Recently, Al-Turk et al (2017) discussed the inference procedures of the unknown parameters of a BGE distribution based on copula functions. Some of the other works related to BGE distribution can be found in Achcar et al (2015), Ibrahim et al (2017), Kundu and Gupta (2011), , Muhammad (2016), Shoaee and Khorram (2012) and the references cited therein.…”

Section: Bge Distributionsmentioning

confidence: 99%

On Bivariate Generalized Exponential-Power Series Class of Distributions

Jafari

Roozegar

2018

JIRSS

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Abstract. In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate generalized exponential-logarithmic, bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as special cases. We derive different properties of the proposed class of distributions. It is observed that the proposed class of bivariate distributions is a very flexible class of distribution functions. The joint probability density functions can have a variety of shapes. It can be bimodal as well as heavy tailed also. This distribution has five parameters. The maximum likelihood estimators of the parameters cannot be obtained in closed form. We propose to use EM algorithm to compute the maximum likelihood estimators of the unknown parameters. It is observed that the proposed EM algorithm can be implemented very easily in practice. One data-set has been analyzed for illustrative purposes. It is observed that the proposed model and the EM algorithm work quite well in practice.

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“…• Poisson-odd exponential uniform by Muhammad (2016b) with F(x) = [1−e −λ(1−e −α(x/(β−x)) ) ]/(1−e −λ ).…”

Section: Real Data Illustrationmentioning

confidence: 99%

Generalized half-logistic Poisson distributions

Muhammad

2017

CSAM

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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.

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Poisson-odd generalized exponential family of distributions: Theory and Applications

Cited by 15 publications

References 39 publications

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

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

On Bivariate Generalized Exponential-Power Series Class of Distributions

Generalized half-logistic Poisson distributions

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