Quantal Response Analysis: enlargement of the logistic model with a kurtosis parameter

Summary

For the estimation of quantiles in tails of distributions the choice of the family of distributions is highly important. In this paper we deal with the distribution function in the model of quantal response analyses, and restrict our attention to the family of the λ ‐distributions ( λ is a kurtosis parameter); a further restriction is obtained by setting λ = 0; we then get the logistic distribution.

The parameter λ is estimated poorly by means of experiment; this parameter, though, is of great importance for the estimation of quantiles in the tail(s) of the distribution.