A Theoretical Basis for Gompertz'S Curve

Makany, Roger Armand

doi:10.1002/bimj.4710330115

Cited by 39 publications

(11 citation statements)

References 7 publications

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“…Recently, many authors have contributed to the statistical methodology and characterization of this distribution. For example, Read [19], Gordon [20], Makany [21], Rao and Damaraju [22], Franses [23] and Wu and Lee [24]. Garg et al [25] studied the properties of the GD and obtained the MLEs for the parameters.…”

Section: The Gd As a Lifetime Modelmentioning

confidence: 99%

Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

İsmail

2010

Journal of Statistical Computation and Simulation

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In this paper, the Bayesian approach is applied to the estimation problem in the case of step stress partially accelerated life tests with two stress levels and type-I censoring. Gompertz distribution is considered as a lifetime model. The posterior means and posterior variances are derived using the squared-error loss function. The Bayes estimates cannot be obtained in explicit forms. Approximate Bayes estimates are computed using the method of Lindley [D.V. Lindley, Approximate Bayesian methods, Trabajos Estadistica 31 (1980), pp. 223-237]. The advantage of this proposed method is shown. The approximate Bayes estimates obtained under the assumption of non-informative priors are compared with their maximum likelihood counterparts using Monte Carlo simulation.

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Section: The Gd As a Lifetime Modelmentioning

confidence: 99%

Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

İsmail

2010

Journal of Statistical Computation and Simulation

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“…According to the literature, the Gompertz distribution was formulated by Gompertz (1825) to fit mortality tables. Many authors have contributed to the statistical methodology and characterization of this distribution (Read 1983;Gordon, 1990;Makany, 1991;Rao and Damaraju, 1992;Franses, 1994;Wu and Lee, 1999). Garg et al (1970) studied the properties of the Gompertz distribution and obtained the maximum likelihood estimates for the parameters.…”

Section: The Gompertz Distributionmentioning

confidence: 99%

Planning step-stress life tests with type-ii censored data

İsmail¹

2011

Sci. Res. Essays

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This study discusses the point and interval estimations of two-parameter Gompertz distribution under partially accelerated life tests with Type-II censoring. Also, the study considers the optimal design problem in the case of time step-stress model. The maximum likelihood estimators and approximate confidence intervals of the model parameters are derived. Also, optimum test plans for the time stepstress life tests are developed. For illustration, a simulation study is provided.

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“…An important characteristic of the Gompertz distribution is that it has an exponentially increasing failure rate for the life of the systems and is often used to model highly negatively skewed data in survival analysis (Johnson and Johnson (1979)). In recent past, many authors have contributed to the studies of statistical methodology and characterization of this distribution; for example, Read (1983), Makany (1991), Rao and Damaraju (1992), Franses (1994), Chen (1997) and Wu and Lee (1999). Garg et al (1970) studied some of the statistical properties of the Gompertz distribution and estimated the parameters using maximum likelihood method with reference to the data on the effects of prolonged oral contraception on mortality in mice.…”

Section: Introductionmentioning

confidence: 99%

Statistical properties and different methods of estimation of Gompertz distribution with application

Dey¹,

Moala

Kumar

2018

Journal of Statistics and Management Systems

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This article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, stochasic ordering, stressstrength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, pseudo-moments estimators, modified moments estimators, L-moment estimators, percentile based estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, minimum spacing

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A Theoretical Basis for Gompertz'S Curve

Abstract: GOMPERTZ'S modcl (18%) hits reni;ritictl ir piircly empirical one, despite its frcquent usagr. A tlicoreticirl justification is given which permits its employment in cases of irccretionary growth.

Cited by 39 publications

References 7 publications

Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring

Planning step-stress life tests with type-ii censored data

Statistical properties and different methods of estimation of Gompertz distribution with application

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