Maximum-Likelihood Estimation of the Parameters of the Gompertz Survival Function

Garg, M. L.; Rao, B. Raja; Redmond, Carol

doi:10.2307/2346545

Cited by 74 publications

(62 citation statements)

References 10 publications

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“…The Weibull model has been used in several applications in engineering, industry and cancer research (Bain, 1978;Laird, 1965). The Gompertz model for γ(x,β) has been used by Garg et al (1970), who have studied its properties and obtained maximum likelihood estimates of its parameters. These distributions can, of course, be generalized by replacing x by x-b, where b represents, what is called the 'guarantee' time in industry, where no item can fail before b units of time have elapsed.…”

Section: Some Preliminariesmentioning

confidence: 99%

Percentile residual life function for a class of life distributions having the "Setting the clock back to zero" property

Rao¹,

Alhumoud²,

Damaraju³

2006

imf

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In the present paper, it is demonstrated that the Percentile Residual Life (PRL) function of a group of individuals in biomedical investigations Ca! easily obtained if the class of their life distributions possesses, what has been called the 'Setting the clock back to zero' property. It is shown that the PRL function for such a family is just its l00(1-α) percentile except, perhaps, with a different vector of parameter values. It is proved that the Gompertzian growth process, Krane's family of distributions and the linear hazard exponential distribution have this property and a simple expression is derived for their PRL function.As a simple application of the main result obtained in the present paper. have utilized a large-scale serial sacrifice experiment by the National Center of Toxicological Research involving 24,000 female mice that were fed 2-AAF from infancy. The number that had developed bladder neoplasms and/or liver neoplasms is available. It is demonstrated that the turnor incidence intensity at time x gives a class of survival models which has the setting the clock back to zero property. Its PRL function is evaluated and tabulated for several choices of parameter values.

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Section: Some Preliminariesmentioning

confidence: 99%

Percentile residual life function for a class of life distributions having the "Setting the clock back to zero" property

Rao¹,

Alhumoud²,

Damaraju³

2006

imf

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“…Consider the random sample 1 , 2 , … , consisting of observations from the ( ; , , , ) distribution having the probability density function given in equation (6). Let = ( , , , ) T be the vector of the parameters.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…The Gompertz distribution has wide applications in demography, actuarial and biological sciences. The maximum likelihood estimates for the parameters of the Gompertz distributional was studied by Garg et al (1970) …”

Section: Introductionmentioning

confidence: 99%

Transmuted Generalized Gompertz distribution with application

Khan¹,

King²,

Hudson³

2017

JSTA

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This paper introduces the four parameter transmuted generalized Gompertz distribution which includes the transmuted Gompertz, transmuted generalized exponential, transmuted exponential, Gompertz, generalized exponential and exponential distributions as special cases and studies its statistical properties. Explicit expressions are derived for the quantile, moments, moment generating function and entropies. Maximum likelihood estimation is used to estimate the model parameters. Finally, two applications of the new distribution is illustrated using reliability data sets.

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“…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. Osman (1987) derived a compound Gompertz model by assuming that one of the parameters of the Gompertz distribution is a random variable following the gamma distribution.…”

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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Maximum-Likelihood Estimation of the Parameters of the Gompertz Survival Function

Cited by 74 publications

References 10 publications

Percentile residual life function for a class of life distributions having the "Setting the clock back to zero" property

Percentile residual life function for a class of life distributions having the "Setting the clock back to zero" property

Transmuted Generalized Gompertz distribution with application

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

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