ABSTRACT
Statistical inferences may be based directly on the order statistics. Since the order statistics are functions of the sample random variables, their joint distribution function can be determined from the likelihood function of the sample. The general shape of the probability distribution function is indicated by plotting a sample histogram or grouped sample frequency distribution. The sample moments may be used to estimate or approximate the population moments. Sufficiency is one possible method of reducing a sample to a few meaningful statistics. This chapter considers problem of obtaining an estimator with good properties from a sample of observations. Choosing to use a minimax estimator is a somewhat pessimistic approach since the estimator is determined by considering the worst possible situations. The maximum likelihood method of estimation is probably overall the most important method of estimation. The chapter discusses the least squares principle of estimation under a different type of model assumption.
