A Lifetime Distribution With an Upside-Down Bathtub-Shaped Hazard Function

Dimitrakopoulou, Theodora; Adamidis, Konstantinos; Loukas, S.

doi:10.1109/tr.2007.895304

Cited by 57 publications

(37 citation statements)

References 9 publications

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“…Dimitrakopoulou et al [11] established a three-parameter lifetime model with PDF ( ; , , ) Journal of Probability and Statistics where > 0 and , > 0 are the shape parameters and > 0 is a scale parameter. The CDF corresponding to (1) is…”

Section: Introductionmentioning

confidence: 99%

The Half-Logistic Generalized Weibull Distribution

Anwar

Bibi

2018

Journal of Probability and Statistics

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A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher's information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

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Section: Introductionmentioning

confidence: 99%

The Half-Logistic Generalized Weibull Distribution

Anwar

Bibi

2018

Journal of Probability and Statistics

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“…Two sets of data is used in the study of Dimitrakopoulou et al, (2007). Depending on the nature of the data sets, they have shown that the estimated hazard function may not always produce bathtub shape curve.…”

Section: Resultsmentioning

confidence: 99%

“…For example, Gaver and Acar (1979) proposed a model that has a broad range of flexibility-constant hazard to bathtub hazard under different conditions, a flexible bathtub hazard model for non-repairable systems with uncensored data (Jaisingh et al, 1987), a lifetime distribution with an upside-down bathtub-shaped hazard function (Dimitrakopoulou et al, 2007) and so on. Mudholkar and Srivastava (1993) introduced an exponentiated Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

New Solution and Its Impact on Increasing, Decreasing and Bathtub Shaped Failure Rate Model

Alam¹

2009

Pak.j.stat.oper.res.

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The maximum likelihood equations of IDB distribution can't be solved analytically. Solutions of the MLE equations can be obtained numerically. But the problem is to detect the initial value of the parameters to solve the nonlinear MLE equations. A technique is developed for formulating the initial value of the parameter to solve the MLE equations of IDB distribution. Considering all the facts, though IDB distribution is not suitable for graduating mortality data but the model can graduate mortality data of Bangladesh in the age range of 0-8 very well.

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“…Example 3: the power generalized Weibull (PGW) distribution ( [4], [20], [21], apparently independently treated in [10]). Probably the simplest direct construct of a tractable hazard function with limiting properties (i) and (ii) is…”

Section: Llslc Distributions With Increasing or Constant Or Decreasinmentioning

confidence: 99%

Log-location-scale-log-concave distributions for survival and reliability analysis

Jones¹,

Noufaily²

2015

Electron. J. Statist.

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Abstract:We consider a novel sub-class of log-location-scale models for survival and reliability data formed by restricting the density of the underlying location-scale distribution to be log-concave. These models display a number of attractive properties. We particularly explore the shapes of the hazard functions of these, LLSLC, models. A relatively elegant, if partial, theory of hazard shape arises under a further minor constraint on the hazard function of the underlying log-concave distribution. Perhaps the most useful LLSLC models are contained in a class of three-parameter distributions which allow constant, increasing, decreasing, bathtub and upsidedown bathtub shapes for their hazard functions.MSC 2010 subject classifications: Primary 62N99; secondary 60E05, 62N05.

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A Lifetime Distribution With an Upside-Down Bathtub-Shaped Hazard Function

Cited by 57 publications

References 9 publications

The Half-Logistic Generalized Weibull Distribution

The Half-Logistic Generalized Weibull Distribution

New Solution and Its Impact on Increasing, Decreasing and Bathtub Shaped Failure Rate Model

Log-location-scale-log-concave distributions for survival and reliability analysis

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