対数正規分布の諸特性の確率紙による推定

概要

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The purpose of this paper is to present the estimation procedures of characteristics of the lognormal distribution using probability paper and todiscuss the bias and efflciency of the estimates. The characteristics are the mode, median and k th root of moment of order k about the origin. These characteristics are in the same units as the variate. The estimation procedure described in this paper is completed with simple geometical operations on the probability paper. The obtained estimate of the characteristics of population, ξ is expressed as ξ=exp(μ^^^+α(σ^^^)^2). Assigning α successively the values α=-1, 0, k/2, we obtain the estimates of the mode,median and k th root of moment of order k where μ^^^ and σ^^^ are the constants proportional to the interception and the inclination of the reglession line on the probability paper. To compute E(ξ)/ξ and Var(ξ)+(E(ξ)-ξ)^2 considering ξ as an estimator, following assumptions are made. (1) In the best case, the estimates μ^^^ and σ^^^ equal to the best linear unbiased estimates of mean and standard deviation of normal distribution by ranking the observations of a sample and taking linear combination of them. (2) In the worst case, the estimates μ^^^ and σ^^^ equal to the mean and range estimate with two observations of a sample.
社団法人日本品質管理学会の論文
1981-10-15