Estimation in Maxwell distribution with randomly censored data

Abstract

In many practical situations, complete data are not available in lifetime studies. Many of the available observations are right censored giving survival information up to a noted time and not the exact failure times. This constitutes randomly censored data. In this paper, we consider Maxwell distribution as a survival time model. The censoring time is also assumed to follow a Maxwell distribution with a different parameter. Maximum likelihood estimators and confidence intervals for the parameters are derived with randomly censored data. Bayes estimators are also developed with inverted gamma priors and generalized entropy loss function. A Monte Carlo simulation study is performed to compare the developed estimation procedures. A real data example is given at the end of the study.

Maximum Likelihood and Bayes Estimation in Randomly Censored Geometric Distribution

“…Since the time required for completing an experiment has a direct impact on the cost, this information is important for an experimenter to choose an appropriate sampling plan. Krishna et al [13] developed ETT for Maxwell distribution under random censoring for the first time. In this section, we develop the mathematical formulation of ETT for randomly censored geometric distribution.…”

“…Rayleigh model with randomly censored data was analyzed by Ghitany [8] and Saleem and Aslam [9]; Burr Type XII was analyzed by Ghitany and Al-Awadhi [10]; generalized exponential and Weibull models were analyzed, respectively, by Danish and Aslam [11,12]. Krishna et al [13] studied Maxwell distribution with randomly censored samples.…”

Estimation of Parameters and Reliability Characteristics in Lindley Distribution Using Randomly Censored Data

“…Kumar and Garg [23] studied estimation of the parameters of randomly censored generalized inverted Rayleigh distribution. Krishna et al [21] discussed estimation in Maxwell distribution with randomly censored data. Garg et al [13] discussed randomly censored generalized inverted exponential distribution.…”

“…For the above integrals in (21) and (22), the closed form solutions are not available. The above integrals can be solved numerically.…”

Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions

“…Dey and Maiti [5] derived Bayes estimators of Maxwell distribution by considering non-informative and conjugate prior distributions under three loss functions, namely, quadratic loss function, squared-log error loss function and MLINEX function. The references [6][7][8] studied the reliability estimation of Maxwell distribution based on Type-II censored sample, progressively Type-II censored sample and random censored sample, respectively. Reference [9] obtained some Bayes estimators under quadratic loss function using non-informative prior, represented by Jefferys prior and Informative priors as Gumbel Type II and Conjugate (Inverted Gamma and Inverted Levy) priors.…”