New Sequential Goodness-of-Fit Test for a Family of Two Parameter Gamma Distributions with Known Shape Based on Skewness and Q-statistic

摘要

The objective of this research is to develop a new goodness-of-fit test for the gamma distribution. The gamma distribution is widely used for reliability and failure time estimations in the real world. Several methods to measure the fit of data to a hypothesized distribution are commonly used such as the chi-squared test, and Anderson- Darling test. The most important aspect of these tests is how well the results reflect the distribution family. This research will use the sequential test with skewness and Q- statistic as test statistics for fitting a gamma distribution. The main idea of a sequential test is that the power of test will be greater than the power of the individual tests. The critical values and significance levels will be created using Monte Carlo simulation. Various power studies against different alternative distributions will be compared to validate the power of the sequential tests.