Minimum Risk Point Estimation of Location Parameter of a Galton Distribution: A Sequential Approach

In this paper we have considered one important distribution useful in Reliability and Life Testing namely, Galton distribution or Lognormal distribution. The lognormal distribution is sometimes called the antilognormal distribution. The name has some logical basis in that it is not the distribution of the logarithm of a normal variable (this is not even always real) but of an exponential ? that is, antilognormal-function of such a variable. It is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. In section I we give a brief introduction to their applications and in section II we explain the problem of estimation of minimum risk point estimation of mean of a Lognormal distribution or Galton distribution and failure of the fixed sample size procedure. In section III sequential solution for this problem have been provided along with study of their asymptotic properties.