Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data

Eliwa, Mohamed S.; El-Morshedy, Mahmoud; Ibrahim, Mohamed

doi:10.1007/s40745-018-0173-0

Cited by 34 publications

(19 citation statements)

References 17 publications

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“…The first four derivatives of Equation (16), with respect to t at t = 0, yield the first four moments about the origin, i.e., E(Z r ) = d r dt r M Z (t)| t=0 . Moreover, utilizing Equation (13) or (16), the skewness (Sk) and kurtosis (Ku) can be expressed as Sk = (µ 3 − 3µ 2 µ 1 + 2µ 3 1 )/(Var) 3/2 and Ku = (µ 4 − 4µ 3 µ 1 + 6µ 2 µ 2 1 − 3µ 4 1 )/(Var) 2 , respectively. In probability theory, the cumulants, say k n , of a probability model are a set of quantities that provide an alternative to the moments of a probability model.…”

Section: Moments Dispersion Index Skewness Kurtosis and Cumulantsmentioning

confidence: 99%

“…In marketing science, it has been used as an individual-level simulation for customer lifetime value modeling. For more details, see Willemse et al [1], Preston et al [2], Melnikov and Romaniuk [3], Ohishi et al [4], Bemmaor et al [5], Cordeiro et al [6], El-Bassiouny et al [7][8][9], Alzaatreh et al [10], Roozegar et al [11], Mazucheli et al [12], Eliwa et al [13], among others.…”

Section: Introductionmentioning

confidence: 99%

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Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

2020

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Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions.

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Section: Moments Dispersion Index Skewness Kurtosis and Cumulantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

2020

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“…Therefore, some extensions or modifications of the G distribution are proposed and studied in the statistical literature to provide more flexibility in lifetime modeling; for example, see [2][3][4][5][6][7][8]. Ref [9] studied and proposed a two-parameter lifetime probability distribution, which is called the inverted Gompertz (IG) distribution, with a hazard rate function, which is an upside-down bathtub-shaped curve. The cumulative distribution function (CDF) and the probability density function (PDF) of the random variable Y that has the IG with the two parameters α > 0 and β > 0 are given, respectively, as (…”

Section: Introductionmentioning

confidence: 99%

Exponentiated Generalized Inverted Gompertz Distribution: Properties and Estimation Methods with Applications to Symmetric and Asymmetric Data

et al. 2021

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In this article, a new four-parameter lifetime model called the exponentiated generalized inverted Gompertz distribution is studied and proposed. The newly proposed distribution is able to model the lifetimes with upside-down bathtub-shaped hazard rates and is suitable for describing the negative and positive skewness. A detailed description of some various properties of this model, including the reliability function, hazard rate function, quantile function, and median, mode, moments, moment generating function, entropies, kurtosis, and skewness, mean waiting lifetime, and others are presented. The parameters of the studied model are appreciated using four various estimation methods, the maximum likelihood, least squares, weighted least squares, and Cramér-von Mises methods. A simulation study is carried out to examine the performance of the new model estimators based on the four estimation methods using the mean squared errors (MSEs) and the bias estimates. The flexibility of the proposed model is clarified by studying four different engineering applications to symmetric and asymmetric data, and it is found that this model is more flexible and works quite well for modeling these data.

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“…Recently, the trend in proposing new bivariate compounded (power series family), weighted and generalized (G-) families of distributions which have received increased attention. See for example, Sunoj and Nair [22], Nair and Sunoj [23], Kundu and Gupta [24], Domma [25], Sarhan et al [26], Kundu and Gupta [27], Barreto-Souza and Lemonte [28], Sarabia et al [29], Balakrishna and Shiji [30], El-Bassiouny et al [31], El-Gohary et al [32], Roozegar and Jafari [33], Ghosh and Hamedani [34], Ibrahim et al [35], Eliwa and El-Morshedy [36], Eliwa et al [37], El-Morshedy et al [38,39] and others.…”

Section: Introductionmentioning

confidence: 99%

Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application

Eliwa

El-Morshedy

2020

Journal of Taibah University for Science

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The aim of our paper is to introduce a new flexible bivariate generalized family of distributions based on Marshall and Olkin shock model, in the so-called the bivariate odd Weibull-G family. The proposed family is constructed from three independent odd Weibull-G families using a minimization process. Creating a bivariate distribution using shock model technique is nothing new, but here, we used only this technique to propose a flexible bivariate family, which has not been considered in the statistical literature yet. Some of its statistical properties are studied. After introducing the general class, one special model of the new family is discussed in detail. Maximum likelihood and Bayesian approaches are used to estimate the model parameters. Further, percentile bootstrap confidence interval and bootstrap-t confidence interval are estimated for the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of the maximum likelihood and Bayesian estimators. Finally, we illustrate the importance of the proposed bivariate family by means of real data set.

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Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data

Cited by 34 publications

References 17 publications

Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications

Exponentiated Generalized Inverted Gompertz Distribution: Properties and Estimation Methods with Applications to Symmetric and Asymmetric Data

Bivariate odd Weibull-G family of distributions: properties, Bayesian and non-Bayesian estimation with bootstrap confidence intervals and application

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