Estimating with percentile grouped and truncated date from a scale parameter distribution

Abstract

Data which is grouped and truncated is considered. We are given numbers n₁<…<n_k=n and we observe X_ni ),i=1,…k, and the tottal number of observations available (N> n_k is unknown. If the underlying distribution has one unknown parameter θ which enters as a scale parameter, we examine the form of the equations for both conditional, unconditional and modified maximum likelihood estimators of θ and N and examine when these estimators will be finite, and unique. We also develop expressions for asymptotic bias and search for modified estimators which minimize the maximum asymptotic bias. These results are specialized tG the zxponential distribution. Methods of computing the solutions to the likelihood equatims are also discussed.

Keywords:

• Truncation
• grouped observations
• scale uarameters
• estimating sample size, asymptotic bias
• maximum likelihood
• Bayes modal estimates