ESTIMATION OF DISTRIBUTION PARAMETERS BY A COMBINATION OF THE BEST LINEAR ORDER STATISTIC METHOD AND MAXIMUM LIKELIHOOD.
Interim scientific report no. 12, Feb 65-Feb 66,
WEIBULL (WALODDI) LAUSANNE (SWITZERLAND)
Pagination or Media Count:
This report consists of three parts, the first one dealing with the unbiased, minimum-variance estimation of location scale parameters, assuming the shape parameter to be known, the second one presenting formulae for computing the likelihood of a given sample, the third one specifying the estimation procedure. The first part developes general formulae for computing the coefficients of linear estimators, composed of all or part of the elements of a random sample. The formulae are specialized for the cases of exponential distributions and also for estimations using two of the order statistics only. Formulae for expected values, variances and covariances of standardized Weibull order statistics are deduced and applied to a system of equations, which determines the linear coefficients. For the solution of such systems, a program has been written and applied to an IBM 7090 computer, which delivers the results extremely fast, thus eliminating the need of extensive tables. The second part presents formulas for computing the likelihood of a given sample for the most general situation, that is, for arbitrarily censored, truncated or grouped samples, and, for the special case of life testing, when the sample may be composed of the subset of items, which have failed after observed time units, a second subset of items, which have accumulated observed time units, without failure, and a third subset of items, which have failed during one or more inspection periods, without knowing their exact life times. The third part defines the procedure of combining the preceding formulas for best estimation, when none of the parameters is known.
- Statistics and Probability