Parameter Estimation of the Gompertz Population

Chen, Zhenmin

doi:10.1002/bimj.4710390111

Cited by 46 publications

(44 citation statements)

References 6 publications

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“…is strictly increasing in c for any c = 0 by using the Lemma 2 of Chen (1997). Moreover, it can also be shown that…”

Section: Resultsmentioning

confidence: 95%

“…Finally, we give a numerical example to illustrate our proposed method. Furthermore, when compared to estimation of Chen (1997), our proposed method can get a better parameter estimation.…”

Section: Introductionmentioning

confidence: 95%

“…For instance, Grag et al (1970) obtained the maximum likelihood estimation of the parameters of the Gompertz distribution, and Gordon (1990) provided the maximum likelihood estimation for mixtures of two Gompertz distributions under censoring. Chen (1997) developed an exact confidence interval and joint confidence region for the parameters of the Gompertz distribution under type II censoring, but he only studied the parameter estimations based on a complete or right censored sample. Hence, in this article, we modify Chen's idea to obtain the exact confidence intervals and joint confidence regions for the parameters of the Gompertz distribution based on doubly type II censored sample.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Estimation of the Parameters of the Gompertz Distribution Based on the Doubly Type II Censored Sample

2004

Qual Quant

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“…is strictly increasing in c for any c = 0 by using the Lemma 2 of Chen (1997). Moreover, it can also be shown that…”

Section: Resultsmentioning

confidence: 95%

“…Finally, we give a numerical example to illustrate our proposed method. Furthermore, when compared to estimation of Chen (1997), our proposed method can get a better parameter estimation.…”

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Estimation of the Parameters of the Gompertz Distribution Based on the Doubly Type II Censored Sample

2004

Qual Quant

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“…This function was originally formulated by Gompertz (1825) for modeling human mortality. A number of authors contributed to the studies of the characterization of this distribution (e.g., Chen, 1997;Wu and Lee, 1999). In the field of water resources, the Gompertz function was adopted by Ouarda et al (1995) to estimate the flood damage in the residential sector.…”

Section: Gompertz Functionmentioning

confidence: 99%

Optimal depth-based regional frequency analysis

Wazneh

Chebana

Ouarda

2013

Hydrol. Earth Syst. Sci.

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Abstract. Classical methods of regional frequency analysis (RFA) of hydrological variables face two drawbacks: (1) the restriction to a particular region which can lead to a loss of some information and (2) the definition of a region that generates a border effect. To reduce the impact of these drawbacks on regional modeling performance, an iterative method was proposed recently, based on the statistical notion of the depth function and a weight function ϕ. This depth-based RFA (DBRFA) approach was shown to be superior to traditional approaches in terms of flexibility, generality and performance. The main difficulty of the DBRFA approach is the optimal choice of the weight function ϕ (e.g., ϕ minimizing estimation errors). In order to avoid a subjective choice and naïve selection procedures of ϕ, the aim of the present paper is to propose an algorithm-based procedure to optimize the DBRFA and automate the choice of ϕ according to objective performance criteria. This procedure is applied to estimate flood quantiles in three different regions in North America. One of the findings from the application is that the optimal weight function depends on the considered region and can also quantify the region's homogeneity. By comparing the DBRFA to the canonical correlation analysis (CCA) method, results show that the DBRFA approach leads to better performances both in terms of relative bias and mean square error.

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“…He studied the properties of compound of Gompertz distribution and suggested its use for modeling lifetime data and analyzing the survivals in heterogeneous populations. Chen (1997) developed an exact confidence interval and an exact joint confidence region for the parameters of the Gompertz distribution under type-II censoring. According to Jaheen (2003), the Gompertz distribution has been used as a growth model, especially in epidemiological and biomedical studies.…”

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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Parameter Estimation of the Gompertz Population

Cited by 46 publications

References 6 publications

Optimal Estimation of the Parameters of the Gompertz Distribution Based on the Doubly Type II Censored Sample

Optimal Estimation of the Parameters of the Gompertz Distribution Based on the Doubly Type II Censored Sample

Optimal depth-based regional frequency analysis

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

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