A lifetime distribution with decreasing failure rate

Adamidis, Konstantinos; Loukas, S.

doi:10.1016/s0167-7152(98)00012-1

Cited by 325 publications

(237 citation statements)

References 12 publications

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“…The elements of J(θ) can be obtained from the author under request. The existence and uniqueness of MLEs of a probability models based on some certain sufficient conditions have been considered in various literature by many researchers, the existence and uniqueness of maximum likelihood estimators of the EP was analyzed by Kuş (2007), for the exponential geometric by Adamidis and Loukas (1998) …”

Section: Estimationmentioning

confidence: 99%

“…The GEP distribution can accommodate decreasing, increasing and upside down bathtub failure rates. Similarly, Adamidis and Loukas (1998) introduced exponential geometric distribution, while Silva et al (2010) come up with the generalized exponential geometric distribution. Tahmasbi and Rezaei (2008) introduced exponential-logarithmic distribution similarly, Pappas et al (2015) proposed a generalized exponential-logarithmic.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized half-logistic Poisson distributions

Muhammad

2017

CSAM

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“…One such class of distributions generated by compounding the well-known lifetime distributions such as exponential, Weibull (W), generalized exponential and exponentiated W with the geometric (Gc) distribution. For example, Adamidis and Loukas (1998) Let be a geometric random variable with probability mass function given by (2) In this paper, we define and study a new lifetime model called the beta generalized inverse Weibull geometric (BGIWGc) distribution. Its main characteristic is that three additional shape parameters are added in Equation (1) to provide more flexibility for the generated distribution.…”

Section: Introductionmentioning

confidence: 99%

The Beta Generalized Inverse Weibull Geometric Distribution

Elbatal¹,

Gebaly²,

Amin³

2017

Pak.j.stat.oper.res.

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A new six-parameter distribution called the beta generalized inverse Weibull-geometric distribution is proposed. The new distribution is generated from the logit of a beta random variable and includes the generalized inverse Weibull geometric distribution. Various structural properties of the new distribution including explicit expressions for the moments, moment generating function, mean deviation are derived. The estimation of the model parameters is performed by maximum likelihood method.

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“…For example, Adamidis and Loukas (1998) proposed a compounding distribution, denoted by exponential geometric (EG) distribution, which properly accommodate survival data in the presence of latent competing risks. Kuş (2007) proposed another compounding distribution that properly accommodates survival data in the presence of latent competing risks and exponential-Poisson distribution (EP).…”

Section: Introductionmentioning

confidence: 99%

Application of the Weibull-Poisson long-term survival model

Vigas

Mazucheli

Louzada

2017

CSAM

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In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponentialPoisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

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A lifetime distribution with decreasing failure rate

Cited by 325 publications

References 12 publications

Generalized half-logistic Poisson distributions

Generalized half-logistic Poisson distributions

The Beta Generalized Inverse Weibull Geometric Distribution

Application of the Weibull-Poisson long-term survival model

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