ESTIMATION FOR THE GENERALIZED POWER SERIES DISTRIBUTION WITH TWO PARAMETERS AND ITS APPLICATION TO BINOMIAL DISTRIBUTION

Publisher Summary This chapter discusses the estimation for the generalized power series distribution (GPSD) with two parameters and its application to binomial distribution. The binomial distribution has essentially two parameters π and n, of which n, is usually known and only π has to be estimated. However, certain cases might arise in which n is unknown, and both n and π have to be estimated. For instance, while experimenting with a radioactive substance, in addition to the mean number (μ = nπ) of disintegrating atoms, it may perhaps be of interest to know the number (n) of atoms capable of disintegration for the substance in fixed intervals of time for some specified solid angle and fit a model correspondingly. The chapter also explains the application of truncated binomial distributions. The computation procedure for simultaneous estimation for the complete binomial is discussed with reference to two examples, one on radioactive disintegrations and the second one on throwing of dice.