Estimation for Mean and Standard Deviation of Normal Distribution under Type II Censoring Kim, Namhyun;
In this paper, we consider maximum likelihood estimators of normal distribution based on type II censoring. Gupta (1952) and Cohen (1959, 1961) required a table for an auxiliary function to compute since they did not have an explicit form; however, we derive an explicit form for the estimators using a method to approximate the likelihood function. The derived estimators are a special case of Balakrishnan et al. (2003). We compare the estimators with the Gupta's linear estimators through simulation. Gupta's linear estimators are unbiased and easily calculated; subsequently, the proposed estimators have better performance for mean squared errors and variances, although they show bigger biases especially when the ratio of the complete data is small.
Asymptotic variances;maximum likelihood estimators;normal distribution;plotting position;type II censoring;
Asgharzadeh, A. (2006). Point and interval estimation for a generalized logistic distribution under progressive type II censoring, Communications in Statistics-Theory and Methods, 35, 1685-1702.
Asgharzadeh, A. (2009). Approximate MLE for the scaled generalized exponential distribution under progressive type-II censoring, Journal of the Korean Statistical society, 38, 223-229.
Balakrishnan, N. (1989). Approximate MLE of the scale parameter of the Rayleigh distribution with censoring, IEEE Transactions on Reliability, 38, 355-357.
Balakrishnan, N. and Asgharzadeh, A. (2005). Inference for the scaled half-logistic distribution based on progressively type II censored samples, Communications in Statistics-Theory and Methods, 34, 73-87.
Balakrishnan, N. and Kannan, N. (2001). Point and interval estimation for the logistic distribution base on progressive type-II censored samples, in Handbook of Statistics, Balakrishnan, N. and Rao, C. R. Eds., 20, 431-456.
Balakrishnan, N., Kannan, N., Lin, C. T. and Ng, H. K. T. (2003). Point and interval estimation for gaussian distribution, Based on progressively type-II censored samples, IEEE Transactions on Reliability, 52, 90-95.
Balakrishnan, N., Kannan, N., Lin, C. T. and Wu, S. J. S. (2004). Inference for the extreme value distribution under progressive type-II censoring, Journal of Statistical Computation and Simulation, 74, 25-45.
Balakrishnan, N. andWong, K. H. T. (1991). Approximate MLEs for the location and scale parameters of the half-logistic distribution with type-II right censoring, IEEE Transactions on reliability, 40, 140-145.
Blom, G. (1958). Statistical Estimates and Transformed Beta Variates, Wiley, New York.
Cohen, A. C. (1959). Simplified estimators for the normal distribution when samples are singly censored or truncated, Technometrics, 1, 217-237.
Cohen, A. C. (1961). Tables for maximum likelihood estimates: Singly truncated and singly censored samples, Technometrics, 3, 535-541.
Cohen, A. C. (1991). Truncated and Censored Samples, Marcel Dekker, Inc., New York.
Gupta, A. K. (1952). Estimation of the mean and standard deviation of a normal population from a censored sample, Biometrika, 39, 260-273.
Harter, H. L. (1961). Expected values of normal order statistics, Biometrika, 48, 151-165.
Hastings, Jr. C., Mosteller, F., Tukey, J.W. andWinsor, C. P. (1947). Low moments for small samples: A comparative study of order statistics, Annals of Mathematical Statistics, 18, 413-426.
Kang, S. B., Cho, Y. S. and Han, J. T. (2008). Estimation for the half logistic distribution under progressively type-II censoring, Communications of the Korean Statistical Society, 15, 367-378.
Kim, C. and Han, K. (2009). Estimation of the scale parameters of the Rayleigh distribution under general progressive censoring, Journal of the Korean Statistical Society, 38, 239-246.
Kim, N. (2014). Approximate MLE for the scale parameter of the generalized exponential distribution under random censoring, Journal of the Korean Statistical Society, 43, 119-131.
Sarhan, A. E. and Greenberg, B. G. (1956). Estimation of location and scale parameters by order statistics from singly and doubly censored sample: Part I. The normal distribution up to size 10, Annals of Mathematical Statistics, 27, 427-451.
Sarhan, A. E. and Greenberg, B. G. (1958). Estimation of location and scale parameters by order statistics from singly and doubly censored sample: Part II. Tables for the normal distribution for samples of size 11 to 15, Annals of Mathematical Statistics, 29, 79-105.
Sarhan, A. E. and Greenberg, B. G., eds. (1962). Contributions to Order Statistics, Wiley, New York.
Seo, E. H. and Kang, S. B. (2007). AMLEs for Rayleigh distribution based on progressively type-II censored data, The Korean Communications in Statistics, 14, 329-344.
Sultan, K. S., Alsada, N. H. and Kundu, D. (2014). Bayesian and maximum likelihood estimation of the inverse Weibull parameters under progressive type-II censoring, Journal of Statistical Computation and Simulation, 84, 2248-265.
Weibull, W. (1939). The phenomenon of rupture in solids, Ingeniors Vetenskaps Akademien Handlingar, 153, 17.