Author(s)

D. Zupan & G. Turk

Abstract

The paper deals with the characteristic value determination from relatively small samples. The characteristic value is usually determined with the assumption that the distribution and its parameters are known. The disadvantages of the method are described and the improved method is presented. Two improved point estimates as well as confidence interval for the characteristic value are presented. All calculations and some of the derivations were performed by computer program Mathematica. 1 Introduction We denote X as a random variable with known cumulative distribution function (CDF) Fx. The characteristic value of the random variable X is the value xa, such that the probability of X being less than z, equals cy: P[X < xa,] = Fx(xa)= a - xa, = Fx-1(a). (1) From eqn (1) follows that characteristic value z, depends on the distribution of random variable X. The characteristic value is usually determined with the assumption that the distribution and its parameters are known, which means that we can exactly describe the CDF. Fx is usually described by two parameters which can be determined from mean mx and standard deviation ox, It is common to many practical problems that the correct values of mx and ox are unknown and can only be estimated from a random sample. Thus, instead of the correct characteristic value, only its estimate could be obtained. The characteristic value estimate is itself a random variable, here denoted as Xa. In the paper the characteristic value estimate is analyzed with respect to the correct value. It is shown that the probability of estimate,

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