A Note On The Estimate Of The Beta Distribution

It is well known that Beta distribution provides the premier family of continuous distributions on bounded support, and there are many distributions based on Beta dis-tribution. In this paper, the lower and upper estimates with explicit coefficients for Beta distribution under a>1,b>1are given. Using variable substitution, we know that Beta distribution of second kind, F distribution and Student’s t distribution have close connection with Beta distribution. Furthermore, using these results, the lower and up-per estimates of Beta distribution of second kind and F distribution, partial estimates of Student’s t distribution are obtained.