On extended type I generalized logistic distribution

The importance of the logistic distribution has already been felt in many areas of human endeavour. Verhulst [12] used it in economic and demographic studies. Berkson [3, 4, 5] used the distribution extensively in analyzing bioassay and quantal response data. The works [6, 9, 10, 11, 8] are a few of many publications on logistic distribution. The simplicity of the logistic distribution and its importance as a growth curve have made it one of the many important statistical distributions. The shape of the logistic distribution that is similar to that of the normal distribution makes it simpler and also profitable on suitable occasions to replace the normal distribution by the logistic distribution with negligible errors in the respective theories. Balakrishnan and Leung [2] show the probability density function of a random variable X that has type I generalized logistic distribution. It is given by fX(x;b)= be −x ( 1+e−x)b+1 , −∞ 0. (1.3)