Unimodality Conditions of the Distribution of a Mixture of Two Distributions
Itsuro Kakiuchi · Institutional Repositories DataBase (IRDB) · 1981
Conditions for which the distribution of a mixture of two normal distributions is unimodal were investigated by Eisenberger [1].To the problem of the pooling of two samples, Takeshita, Kasagi and Yanagawa [4], and Inada and Kakiuchi [2] employed unimodality conditions of the distribution of the pooled samples.We may be especialy interested in whether a distribution is unimodal or bimodal because the information contained in this fact alone may be more important than the parameters of the actual distribution.In this paper we consider the distribution of a mixture of two distributions without the assumption of the normality and investigate a critical value of the differrence between means of two distributions for which the distribution is unimodal for any proportions p and 1-p, 0 < p < 1.In section 1, when only means are different, the critical value which is independent of pis obtained.In section 2, when both means and variances are different, some results in section 1 are extended, and a condition of the shape of the probability density function of the individual distribution for which the distribution is never unimodal is obtained.For the normal, 3 l 5