Some Discrete Lifetime Distributions with Bathtub-Shaped Hazard Rate Functions

Noughabi, M. Shafaei; Roknabadi, A. H. Rezaei; Borzadaran, Gholam Reza Mohtashami

doi:10.1080/08982112.2013.769055

Cited by 23 publications

(11 citation statements)

References 21 publications

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“…log ψ(q, µ i ) log q log q x i +1 − q − ψ(q, µ i ) log q log q x i − 1 , (14) where ψ(q, µ i ) = (1 − q)((1 + µ i )q − µ i ). Equation ( 14) is not in closed form and it cannot be solved explicitly.…”

Section: Trtg Count Regression Modelmentioning

confidence: 99%

“…The simulation results were determined to explore their performance in estimating the TRTG parameters θ and q. The applicability of the TRTG distribution was studied by three data sets from the actuarial sciences showing its superiority as compared with competing models, namely transmuted geometric [13], discrete Burr [3], discrete Chen [14], negative binomial, geometric, and Poisson distributions. We were also motivated to propose a count regression model based on the TRTG distribution.…”

Section: Introductionmentioning

confidence: 99%

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A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

et al. 2021

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In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regression model. These applications showed empirically that the TRTG distribution outperforms some important discrete models such as the negative binomial, transmuted geometric, discrete Burr, discrete Chen, geometric, and Poisson distributions.

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Section: Trtg Count Regression Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

et al. 2021

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“…Illustration of how such models arise in practice and their justification in the case of biological organisms and mechanical devices are provided in Marshall and Olkin [9]. Jiang [7], Noughabi et al [12], Noughabi et al [13], Bebbington et al [2] and Almalki and Nadarajah [1] present a variety of discrete life distributions that represent real data possessing BT hazard rate functions. On the other hand, UBT models have an increasing hazard rate initially, followed by one with constant and then a decreasing hazard rate.…”

Section: Introductionmentioning

confidence: 99%

Some properties of discrete bathtub-shaped distributions

Nair

Sankaran

Ramesh

2016

Communications in Statistics - Theory and Methods

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The existence and the usefulness of discrete bathtub-shaped and upside down bathtubshaped distributions have been demonstrated in some papers of recent origin. However, the general properties of these two classes of distributions do not seem to have been discussed. This paper proposes to study some reliability properties of such distributions. We investigate the closure properties with reference to convolution, mixing, series and parallel systems, etc. and existence of bounds on reliability functions, moment properties and convergence.

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“…Recently, several continuous distributions have been discretized for modeling lifetime data, such as those summarized in Table 1. Discrete Chen Noughabi et al [7] On the other hand, a natural discrete analog of the continuous Lindley model, called natural discrete Lindley (NDL), was introduced by [8] as a mixture of the negative binomial and geometric distributions. Several reliability properties of the NDL were explored by [9].…”

Section: Introductionmentioning

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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Some Discrete Lifetime Distributions with Bathtub-Shaped Hazard Rate Functions

Cited by 23 publications

References 21 publications

A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

Some properties of discrete bathtub-shaped distributions

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

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