Statistical distributions and their application
Date
1956
Authors
Das, Sadhu Charan
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Chapters 1 and 2 are concerned with a problem of curve fitting which arose in testing the hypothesis pro posed by Bowen(1953) concerning daily rainfall data.
Chapter 1. The method of maximum likelihood has been used to fit a truncated type III (Gamma) distribution to daily rainfall data for Sydney over the period 1859-1952. An approximate test of the hypothesis that there is a singularity at the origin is suggested. This test is based on a comparison of the expected frequency in the truncated part, when the observed frequency in this part is taken into account in the fit, with the expected frequency when these observations are neglected. For Sydney data the test shows that there is no evidence in the rainfall data for a singularity at the origin.
Chapter 2. Meteorologists usually consider a lognormal curve to be appropriate for graduating rainfall data. Accordingly in this chapter we discuss the fitting of a log-
normal distribution to the above daily rainfall data for Sydney The method used in fitting is also that of maximum likelihood. As judged by the X^2 test, the fit does not compare well with that previously obtained by the use of a type III distribution.
Chapter 3 discusses the numerical evaluation of a certain class of integrals, which is connected with some of the work done in the first two chapters. In calculating the expected frequencies as given in the column headed f1 of the table 2 in the second chapter, use was made of the univariate normal probability integrals. These are well known, but the similar integrals in the multivariate cases are difficult to evaluate; we devise an elementary method of evaluating normal probability integrals for the bivariate, and trivariate cases. A short discussion of the general multivariate case is also given, and this method is then applied to the univariate case as an alternative to the known methods.
Description
Keywords
Distribution (Probability theory)
Citation
Collections
Source
Type
Thesis (PhD)