Discriminating between generalized exponential, geometric extreme exponential and Weibull distributions

Pakyari, Reza

doi:10.1080/00949650903173306

Cited by 21 publications

(8 citation statements)

References 12 publications

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“…Data consist of the failure times of the air conditioning system of an airplane (Linhart and Zucchini, 1986). They are 23,261,87,7,120,14,62,47,225,71,246,21,42,20,5,12,120,11,3,14,71,11,14,11,16, 90, 1, 16, 52, 95 and already used by Pakyari (2014). The maximum likelihood estimates of the parameters of Tw 2 (m, φ) and GTw 2 ( m, φ) distributions are calculated as m = 59.60, φ = 1.2317, m = 59.60 and φ = 0.2380.…”

Section: Failure Times Of the Air Conditioning Systemmentioning

confidence: 99%

“…The second dataset concerns the time to failure of sixty-one cam-driven reciprocating pumps used in the submarine distillation system over the observation period beginning in May 1987 and ending in December 1993. They are as follows: 1, 2, 2, 2, 3,4,5,8,10,11,13,13,15,17,18,26,27,29,10,14,14,18,21,24,28,31,34,38,41,61,15,21,23,26,33,41,43,43,56,10,25,39,42,48,52,24,26,34,43,44,49,51,37,40, 0, 0, 0, 0, 0, 0, 0. The source of data ...…”

Section: Time To Failure Of Pumpsmentioning

confidence: 99%

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Discriminating between and within (semi)continuous classes of both Tweedie and geometric Tweedie models

Abid¹,

Kokonendji²

2020

Preprint

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In both Tweedie and geometric Tweedie models, the common power parameter p (0, 1) works as an automatic distribution selection. It mainly separates two subclasses of semicontinuous (1 < p < 2) and positive continuous (p ≥ 2) distributions. Our paper centers around exploring diagnostic tools based on the maximum likelihood ratio test and minimum Kolmogorov-Smirnov distance methods in order to discriminate very close distributions within each subclass of these two models according to values of p. Grounded on the unique equality of variation indices, we also discriminate the gamma and geometric gamma distributions with p = 2 in Tweedie and geometric Tweedie families, respectively. Probabilities of correct selection for several combinations of dispersion parameters, means and sample sizes are examined by simulations. We thus perform a numerical comparison study to assess the discrimination procedures in these subclasses of two families. Finally, semicontinuous (1 < p ≤ 2) distributions in the broad sense are significantly more distinguishable than the over-varied continuous (p > 2) ones; and two datasets for illustration purposes are investigated.

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Section: Failure Times Of the Air Conditioning Systemmentioning

confidence: 99%

Section: Time To Failure Of Pumpsmentioning

confidence: 99%

Discriminating between and within (semi)continuous classes of both Tweedie and geometric Tweedie models

Abid¹,

Kokonendji²

2020

Preprint

View full text Add to dashboard Cite

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“…The distribution has received a great attention by researchers. For example, various properties and comparison with other distributions have been provided by different researchers such as: [13], [12,14,15,16,17,18,19,20,21,22,23,24,25] and [26] to mention but a few. Also, this distribution have been extended by different researcher.…”

Section: Introductionmentioning

confidence: 99%

Inferences on the Weibull Exponentiated Exponential Distribution and Applications

Usman¹,

Suleiman²,

Arkilla³

et al. 2020

IJSDA

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In this article, an alternative method of defining the probability density function of Generalized Weibull-exponential distributions is proposed. Based on the method, the distribution can also be called Weibull exponentiated exponential distribution. This distribution includes the exponential, Weibull and exponentiated exponential distributions as special cases. Comprehensive mathematical treatment of the distribution is provided. The quantile function, mode, characteristic function, moment generating function among other mathematical properties of the distribution were derived. The parameters of the distribution were estimated by applying the Maximum Likelihood Procedure.The elements of the Fisher Information Matrix is also provided. Finally, a data set is fitted to the model and its sub-models. It is observed that the new distribution is more flexible and can be used quiet effectively in analysing real life data in place of exponential, Weibull and exponentiated exponential distributions.

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“…Ashour and Hashish [22] provided a numerical comparison study for using RML-procedure, S-procedure, and F-procedure in failure model discrimination. Pakyari [23] presented diagnostic tools based on the likelihood ratio test and the minimum Kolmogorov distance method to discriminate between the generalized exponential, geometric extreme exponential, and Weibull distributions. Elsherpieny et al [24] provided a method to discriminate the gamma and log-logistic distributions based on progressive type II censored data.…”

Section: Introductionmentioning

confidence: 99%

Model Selection Approaches for Predicting Future Order Statistics from Type II Censored Data

Chiang

Wang

Tsai

et al. 2018

Mathematical Problems in Engineering

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This paper studies a discriminant problem of location-scale family in case of prediction from type II censored samples. Three model selection approaches and two types of predictors are, respectively, proposed to predict the future order statistics from censored data when the best underlying distribution is not clear with several candidates. Two members in the location-scale family, the normal distribution and smallest extreme value distribution, are used as candidates to illustrate the best model competition for the underlying distribution via using the proposed prediction methods. The performance of correct and incorrect selections under correct specification and misspecification is evaluated via using Monte Carlo simulations. Simulation results show that model misspecification has impact on the prediction precision and the proposed three model selection approaches perform well when more than one candidate distributions are competing for the best underlying distribution. Finally, the proposed approaches are applied to three data sets.

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Discriminating between generalized exponential, geometric extreme exponential and Weibull distributions

Cited by 21 publications

References 12 publications

Discriminating between and within (semi)continuous classes of both Tweedie and geometric Tweedie models

Discriminating between and within (semi)continuous classes of both Tweedie and geometric Tweedie models

Inferences on the Weibull Exponentiated Exponential Distribution and Applications

Model Selection Approaches for Predicting Future Order Statistics from Type II Censored Data

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