PARAMETER ESTIMATION BASED ON GROUPED OR CONTINUOUS DATA FOR TRUNCATED EXPONENTIAL DISTRIBUTIONS

摘要

Parameter estimation based on truncated data is dealt with; the data are assumed to obeytruncated exponential distributions with a variety of truncation time—a1 data are obtainedby truncation time b1, a2 data are obtained by truncation time b2 and so on, whereas theunderlying distribution is the same exponential one. The purpose of the present paper is togive existence conditions of the maximum likelihood estimators (MLEs) and to show someproperties of the MLEs in two cases: 1) the grouped and truncated data are given (that is,the data each express the number of the data value falling in a corresponding subinterval),2) the continuous and truncated data are given.