Statistical Inference for Gompertz Distribution based on Progressive Type-II Censored Data with Binomial Removals

Manoj Chacko, Rakhi Mohan

Abstract


In this paper, the problem of estimation of parameters for a two-parameterGompertz distribution is considered based on a progressively type-II censored sample with binomial removals. Together with the unknown parameters, the removal probability is also estimated. The maximum likelihood estimators of the parameters and the asymptotic variance-covariance matrix of the estimates are obtained. Bayes estimators are also obtained using different loss functions such as squared error, LINEX and general entropy. A simulation study is performed for comparison between various estimators developed in this paper. A real data set is also used for illustration.


Keywords


Gompertz distribution; Progressive type-II censoring; Binomial removals; Bayes estimates; MCMC method

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References


R. AGGARWALA, N. BALAKRISHNAN (1996). Recurrence relations for single and product moments of progressive type-II right censored order statistics from exponential and truncated exponential distributions. Annals of the Institute of Statistical Mathematics, 48, no. 4, pp. 757–771.

R. AGGARWALA, N. BALAKRISHNAN (1998). Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. Journal of Statistical Planning and Inference, 70, no. 1, pp. 35–49.

B. AL-ZAHRANI (2012). Maximum likelihood estimation for generalized Pareto distribution under progressive censoring with binomial removals. Open Journal of Statistics, 2, no. 04, pp. 420–423.

Z. H. AMIN (2008). Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals. Journal of Applied Statistics, 35, no. 11, pp. 1203–1217.

R. AZIMI, B. FASIHI, F. A. SARIKHANBAGLU (2014). Statistical inference for generalized Pareto distribution based on progressive type-II censored data with random removals. International Journal of ScientificWorld, 2, no. 1, pp. 1–9.

R. AZIMI, F. YAGHMAEI (2013). Bayesian estimation based on Rayleigh progressive type II censored data with binomial removals. Journal of Quality and Reliability Engineering, 2013, pp. 1–6.

N. BALAKRISHNAN, R. R. SANDHU (1996). Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive type-II censored samples. Sankhya: The Indian Journal of Statistics, Series B, 58, no. 1, pp. 1–9.

M. CHACKO, R. MOHAN (2017). Estimation of parameters of Kumaraswamy-exponential distribution under progressive type-II censoring. Journal of Statistical Computation and Simulation, 87, no. 10, pp. 1951–1963.

Z. CHEN (1997). Parameter estimation of the Gompertz population. Biometrical Journal, 39, no. 1, pp. 117–124.

N. FEROZE, I. EL-BATAL (2013). Parameter estimations based on Kumaraswamy progressive type II censored data with random removals. Journal of Modern Applied Statistical Methods, 12, no. 2, p. 19.

B. GOMPERTZ (1825). XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. Frs &c. Philosophical transactions of the Royal Society of London, 115, pp. 513–583.

R. G. MILLER (1981). Survival Analysis. JohnWilley & Sons, New York.

R. MOHAN, M. CHACKO (2016). Estimation of parameters of Gompertz distribution under progressive type-II censoring. The Kerala Statistical Association, 27, pp. 84–103.

J. H. POLLARD, E. J. VALKOVICS (1992). The Gompertz distribution and its applications. Genus, pp. 15–28.

A. SHANUBHOGUE, N. R. JAIN (2013). Minimum variance unbiased estimation in the Gompertz distribution under progressive type II censored data with binomial removals. ISRN Probability and Statistics.

V. K. SHARMA (2018). Estimation and prediction for type-II hybrid censored data follow flexible Weibull distribution. Statistica, 77, no. 4, pp. 385–414.

S. K. SINGH, U. SINGH, V. K. SHARMA, M. KUMAR (2015). Estimation for flexible Weibull extension under progressive type-II censoring. Journal of Data Science, 13, no. 1, pp. 21–41.

M. A. STEPHENS (1974). Edf statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, no. 347, pp. 730–737.

S. K. TSE, C. YANG, H. K. YUEN (2000). Statistical analysis of Weibull distributed lifetime data under type II progressive censoring with binomial removals. Journal of Applied Statistics, 27, no. 8, pp. 1033–1043.

R. VIVEROS, N. BALAKRISHNAN (1994). Interval estimation of parameters of life from progressively censored data. Technometrics, 36, no. 1, pp. 84–91.

C. C. WU, S. WU, H. Y. CHAN, et al. (2004). MLE and the estimated expected test time for Pareto distribution under progressive censoring data. International Journal of Information and Management Sciences, 15, no. 3, pp. 29–42.

S. WU, C. T. CHANG (2003). Inference in the Pareto distribution based on progressive type II censoring with random removals. Journal of Applied Statistics, 30, no. 2, pp. 163–172.

H. K. YUEN, S. K. TSE (1996). Parameters estimation for Weibull distributed lifetimes under progressive censoring with random removals. Journal of Statistical Computation and Simulation, 55, no. 1-2, pp. 57–71.




DOI: 10.6092/issn.1973-2201/7847