Discrete Burr-Hatke Distribution With Properties, Estimation Methods and Regression Model

Elmorshedy, Mahmoud F.; Eliwa, Mohamed S.; Altun, Emrah

doi:10.1109/access.2020.2988431

Cited by 56 publications

(26 citation statements)

References 17 publications

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“…In this section, the UPA distribution is fitted to three real biological datasets and compared with the discrete Burr-Hatke (DBH) [21], discrete Poisson Lindley (DPL) [22], natural discrete Lindley (NDL) [8], discrete Pareto (DP) [5], PA and Poisson distributions according to the model's ability. The first dataset (Catcheside et al [23]) refers to numbers of chromatid aberrations, and it was adopted by Hassan et al [15] for comparing the Poisson and PA distributions.…”

Section: Modeling Biological Datamentioning

confidence: 99%

The Uniform Poisson–Ailamujia Distribution: Actuarial Measures and Applications in Biological Science

et al. 2021

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We propose a new asymmetric discrete model by combining the uniform and Poisson–Ailamujia distributions using the binomial decay transformation method. The distribution, named the uniform Poisson–Ailamujia, due to its flexibility is a good alternative to the well-known Poisson and geometric distributions for real data applications in public health, biology, sociology, medicine, and agriculture. Its main statistical properties are studied, including the cumulative and hazard rate functions, moments, and entropy. The new distribution is considered to be suitable for modeling purposes; its parameter is estimated by eight classical methods. Three applications to biological data are presented herein.

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Section: Modeling Biological Datamentioning

confidence: 99%

The Uniform Poisson–Ailamujia Distribution: Actuarial Measures and Applications in Biological Science

et al. 2021

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“…In this section, we use three real data sets to illustrate the importance and superiority of the NDL distribution over the existing models, namely discrete Lindley (DL) [ 16 ], discrete Burr (DB), geometric (Gc), discrete Pareto (DP) [ 6 ], and discrete Burr-Hatke (El-Morshedy et al [ 32 ]) distributions. The first dataset consists of remission times in weeks for 20 leukemia patients randomly assigned to a certain treatment (Lawless [ 33 ]).…”

Section: Applications To Count Datamentioning

confidence: 99%

A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications

Al-Babtain

Ahmed

Afify

2020

Entropy

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In this paper, we propose and study a new probability mass function by creating a natural discrete analog to the continuous Lindley distribution as a mixture of geometric and negative binomial distributions. The new distribution has many interesting properties that make it superior to many other discrete distributions, particularly in analyzing over-dispersed count data. Several statistical properties of the introduced distribution have been established including moments and moment generating function, residual moments, characterization, entropy, estimation of the parameter by the maximum likelihood method. A bias reduction method is applied to the derived estimator; its existence and uniqueness are discussed. Applications of the goodness of fit of the proposed distribution have been examined and compared with other discrete distributions using three real data sets from biological sciences.

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“…The variance and dispersion index (DI) of the DLi-3P distribution are given, respectively, by (14) and (15), as shown at the bottom of the next page. The skewness and kurtosis can be derived also in explicit forms by using the below quantities.…”

Section: B Moments Skewness Kurtosis and Dispersion Indexmentioning

confidence: 99%

“…Hereafter, (31) is called as the INAR(1)DLi-3P process. The mean, variance and DI of the INAR(1)DLi-3P process can be easily computed by replacing µ ε , σ 2 ε and DI ε in (28), (29) and (30) with (10), (14) and (15), respectively. Since the DLi-3P distribution has an ability to model underdispersion, equi-dispersion and over-dispersion simultaneously, the INAR(1)DLi-3P will be good candidate to model all kind of dispersed time series of counts.…”

Section: Inar(1)dli-3p Processmentioning

confidence: 99%

A New Three-Parameter Discrete Distribution With Associated INAR(1) Process and Applications

et al. 2020

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The aim of this article is to propose a new three-parameter discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, index of dispersion, mean residual life, mean past life and stress-strength reliability. These properties are expressed in explicit forms. The maximum likelihood approach is used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of the estimators. Using the proposed distribution, a new first-order integervalued autoregressive process is introduced for the over-dispersed, equi-dispersed and under-dispersed time series of counts. To demonstrate the importance of the proposed distribution, three data sets on coronavirus, length of stay at psychiatric ward and monthly counts of larceny calls are analyzed. INDEX TERMS Survival discretization method, over-dispersion, INAR(1) process, simulation.

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Discrete Burr-Hatke Distribution With Properties, Estimation Methods and Regression Model

Cited by 56 publications

References 17 publications

The Uniform Poisson–Ailamujia Distribution: Actuarial Measures and Applications in Biological Science

The Uniform Poisson–Ailamujia Distribution: Actuarial Measures and Applications in Biological Science

A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications

A New Three-Parameter Discrete Distribution With Associated INAR(1) Process and Applications

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