Samuel S. Shapiro

The Johnson System: Selection and Parameter Estimation

This paper presents simple criteria which can be used to select which of the three members of the Johnson System of distributions should be used for fitting a set of data. The paper also presents elementary formulas for estimating the parameters for each of the members of the family. Thus, many obstacles to the use of the Johnson System are resolved.

A Regression Test for Exponentiality: Censored and Complete Samples

Two new tests for the two-parameter exponential distribution are presented. The test statistics can be used with doubly censored samples, are easy to compute, need no special constants, and have high power compared with several competing tests. The first test statistic is sensitive to monotone hazard functions, and its percentage points can be closely approximated by the standard normal distribution. The second test statistic is sensitive to nonmonotone hazard functions. The chi-squared (2 degrees of freedom) distribution can be used as an approximation to the distribution of this statistic for moderate and large sample sizes. Monte Carlo power estimates and an example are given.

An alernative test for normality based on normalized spacings

The Shapiro-Wilk statistic and its modifications are widely used for assessing the assumption that a sample was drawn from a normal distribution. Many of the modifications simplified the calculation of the test statistic but resulted in a loss of power. In this paper, we propose an alternative statistic for testing normality which is easy to compute and has power comparable or superior to the original W test.

A Review of Distributional Testing Procedures and Development of a Censored Sample Distributional Test

A review of recent procedures for tests of distributional assumptions is given. Test procedures are grouped into three categories: regression type tests, probability integral transformation tests and special feature tests. The application of regression tests to distributions with location and shape parameters with emphasis on the normal, multivariate normal, exponential, and Weibull distributions and the advantages and limitations of recently improved EDF procedures are discussed. Tests which use characteristics unique to each of the normal, exponential, gamma, extreme value and Weibull distributions are also discussed.

Bernoulli trials and discrete distributions

This tutorial paper defines a process in terms of Bernoulli random variables and develops a number of discrete distributions based on this formulation. The distributions are the binomial, geometric, hypergeometric, negative binomial, beta-binomial, mult..

W-test for the Weibull distribution

A new goodness-of-fit test for the two-parameter Weibull distribution or extreme-value (smallest element) distribution with unknown parameters is presented in this paper. The test statistic is based on similar principles used in the derivation of the well known W test for normality. The test statistic is simple to compute and requires no table of constants. Percentiles and power for a wide variety of alternative distributions are estimated via simulation. A comparison of the proposed test with the Mann-Scheuer-Fertig procedure shows that the power of the test for the former is as high or higher than that for the latter.

Composite Tests For The Gamma Distribution

In this paper we discuss testing the hypothesis that a random sample can be modeled by a gamma distribution for the case of a known or unknown shape parameter. We introduce a new test, one based on the modified Greenwood statistic, and compare this with two presently available tests, Anderson-Darling and Locke. In this paper we emphasize how to use each of the three tests, and, based on the results of a simulation study, we recommend under what conditions each should be used.

SELECTING FAILURE MONITORING TIMES FOR AN EXPONENTIAL LIFE DISTRIBUTION

In certain situations in life testing, it is more practical to record whether a unit fails in an interval instead of measuring failure times exactly. This paper considers the analysis of life data from the exponential distribution with the use of period..

Goodness-of-Fit Tests for Pareto Distribution

The Pareto distribution can serve to model several types of datasets, especially those arising in the insurance industry. In this chapter, we present methods to test the hypothesis that the underlying data come from a Pareto distribution. The tests presented for both the type I and type II Pareto distributions are based on the regression test of Brain and Shapiro (1983) for the exponential distribution. Power comparisons of the tests are carried out via simulations.

Estimating the Mean of an Exponential Distribution from Grouped Observations

In a number of industrial situations, it is more economical to record the number of observations within preset categories instead of recording the observations exactly. using more than two categories serves as a good alternative to dichotomous data, suc..