級分け観測値に対するベキ正規分布のあてはめ

抄録

In medical science and biology, individuals are divided into the group in advance by some criteria, and statistical processing are often carried out on grouped observations of the individuals. In this case, the midpoint in the interval into which a group is divided is handled as a representative value, and some corrections such as Sheppard may be used, to calculate some statistics or quantities such as mean and variance. However, this procedure may not be sometime appropriate in practice because the numbers of intervals were often small or the lengths of intervals were not uniform. So, the probability that the observed value belongs to the interval is obtained by supposing some underlying distributions, which are appropriate for describing the phenomenon. Thus, the likelihood can be cnstructed and the inference about parameters of distribution can be carried out based on the likelihood. In practice, it is desirable that the inference can be carried out on the family of the distributions or data-adaptive distribution which include underlying distributions, if it were possible, normal distribution with historical and statistical “property”. In this paper, when underlying distributions are unknown, power normal distribution, which includes normal distribution, was adopted. Further, unstructured data were used in this investigation, as it is caught specifically to fit power normal distribution to grouped observations. Through some examples cited form published literature and simulated data, it was shown that interpretation and consideration could be done by using the property of normal distribution intended after the transformation of observation, by performing statistical processing on transformed scale, and inverse-transforming to original scale, that is, returning to original scale of the power normal distribution.