The Outliers of Mixed Observations

Abstract

We consider a mixed set of observations consisting of the elements of two samples with different distribution functions. We treat the first sample as a basic sample, the second as outliers. The probability that any order statistic of the mixed sample is from the second sample is calculated. Taking into account this probability, a new empirical distribution function of a mixed sample is defined by giving a small weight to the order statistic if the probability that it is an outlier is greater. The estimation of parameters are described using the classical substitution method, i.e., the substitution of the theoretical distribution function with the empirical distribution function. Some applications in reliability are discussed.