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A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings

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A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings

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Author : Mark C. Coppa
language : en
Publisher:
Release Date : 1993

A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings written by Mark C. Coppa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

The critical values for a new goodness-of-fit test based on spacings are generated for the Weibull distribution when the shape parameter is known. The critical values are used for testing whether a set of observations follow a Weibull distribution when the scale and location parameters are unknown. A Monte Carlo simulation with 10,000 iterations is used to generate the critical values for sample sizes 5(5)35 at shape parameters k equal to 0.5(0.5)1.5 and for sample sizes 5(5)20 at shape parameters k = 2.0(1.0)4.0. A Monte Carlo power study of the Z* test statistic using 5000 iterations is accomplished using nine alternate distributions H sub A. The power is good to excellent when the null hypothesis Ho is from a skewed distribution(k 2.0). Power results at shape parameters k 2.0 are poor for all sample sizes considered. A comparison is made, at shape parameter 1.0, against the prominent competing goodness-of-fit test statistics. Data is obtained from a prior AFIT thesis by Bush. Results indicate that the Z* test is more powerful than the competition at the available sample sizes of 5, 15 and 25 and alpha levels: 0.05 and 0.01. A relationship between the critical value and the sample size is investigated to allow for greater usage of the test statistic. Satisfactory values of fit are attained with a simple log-linear relationship ... Goodness-of-Fit Test, Weibull Distribution, Spacings.

A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings

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Author : Mark C. Coppa
language : en
Publisher:
Release Date : 1993

A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings

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Author : Mark Charles Coppa (CAPT, USAF.)
language : en
Publisher:
Release Date : 1993

A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings written by Mark Charles Coppa (CAPT, USAF.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Goodness-of-fit tests categories.

Anderson Darling And Cramer Von Mises Based Goodness Of Fit Tests For The Weibull Distribution With Known Shape Using Normalized Spacings

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Author : Eric William Frisco
language : en
Publisher:
Release Date : 1998-03-01

Anderson Darling And Cramer Von Mises Based Goodness Of Fit Tests For The Weibull Distribution With Known Shape Using Normalized Spacings written by Eric William Frisco and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-01 with Goodness-of-fit tests categories.

Two new goodness-of-fit tests are developed for the three-parameter Weibull distribution with known shape parameter. These procedures eliminate the need for estimating the unknown location and scale parameters prior to initiating the tests and are easily adapted for censored data. This is accomplished by employing the Anderson-Darling and Cramer-von Mises statistics based on the normalized spacings of the sample data. Critical values of the new tests are obtained for common significance levels by large Monte Carlo simulations for shapes 0.5(0.5)4.0 and sample sizes 5(5)40 with up to 40% censoring (Type II) from the left and/or right. An extensive Monte Carlo power study is also conducted to compare the two tests with each other and with their prominent competitors. The competitors include another spacings test, Z*, and the modified Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling EDF tests. Results show the Anderson-Darling spacings test is the preferred test for the three-parameter Weibull distribution with known shape parameter.

Two And Three Parameter Weibull Goodness Of Fit Tests

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Author : James W. Evans
language : en
Publisher:
Release Date : 1989

Two And Three Parameter Weibull Goodness Of Fit Tests written by James W. Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematical statistics categories.

A New Sequential Goodness Of Fit Test For The Three Parameter Weibull Distribution With Known Shape Based On Skewness And Kurtosis

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Author : Jonathan C. Clough
language : en
Publisher:
Release Date : 1998-03-01

A New Sequential Goodness Of Fit Test For The Three Parameter Weibull Distribution With Known Shape Based On Skewness And Kurtosis written by Jonathan C. Clough and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-01 with Goodness-of-fit tests categories.

The Weibull distribution finds wide applicability across a broad spectrum of disciplines and is very prevalent in reliability theory. Consequently, numerous statistical tests have been developed to determine whether sample data can be adequately modeled with this distribution. Unfortunately, the majority of these goodness-of-fit tests involve a substantial degree of computational complexity. The study presented here develops and evaluates a new sequential goodness-of-fit test for the three-parameter Weibull distribution with a known shape that delivers power comparable to popular procedures while dramatically reducing computational requirements. The new procedure consists of two distinct tests, using only the sample skewness and sample kurtosis as test statistics. Critical values are derived using large Monte Carlo simulations for known shapes k=0.5(0.5)4 and sample sizes n=5(5)50. Attained significance levels for all combinations of the two tests between alpha=0.01(0.01)0.20 are also are approximated with Monte Carlo simulations and presented in a useful contour plot format. Extensive power studies against numerous alternate distributions demonstrate the test's excellent performance compared to popular EDF test statistics such as the Anderson-Darling and Cramer- von Mises tests. Recommendations are included on techniques to chose significance levels of the two component tests in a manner that should optimize power while maintaining the overall significance level.

A New Sequential Goodness Of Fit Test For The Three Parameter Weibull Distribution With Known Shape Parameter Value Based On Skewness And Q Statistic G O F Test Statistics

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Author : Tibet Memis (1LT, TUAF.)
language : en
Publisher:
Release Date : 1999

A New Sequential Goodness Of Fit Test For The Three Parameter Weibull Distribution With Known Shape Parameter Value Based On Skewness And Q Statistic G O F Test Statistics written by Tibet Memis (1LT, TUAF.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

A New Sequential Goodness Of Fit Test For The Three Parameter Weibull Distribution With Known Shape Parameter Value Based On Skewness And Q Statis G O F Test Statistics

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Author : Tibet Memis
language : en
Publisher:
Release Date : 1999-03-01

A New Sequential Goodness Of Fit Test For The Three Parameter Weibull Distribution With Known Shape Parameter Value Based On Skewness And Q Statis G O F Test Statistics written by Tibet Memis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-01 with categories.

Due to its flexibility, the Weibull distribution has very wide applicability in a lot of disciplines and is very prevalent in reliability theory. Thus, a lot of statistical tests that generally have a substantial degree of computional complexity have been developed to determine if the data at hand can be represented with this distribution. This research presents a new omnibus goodness-of-fit test (G.O.F.) that has less computational complexity than the existing tests for the three-parameter Weibull distribution using a sequential application of two individual tests, sample skewness and Q-Statistic. A Monte Carlo procedure has been employed to generate critical values for the skewness and Q-Statistic (G.O.F.) tests for various Weibull distributions with specified shape parameter values. Additionally, tables or charts of attained significance levels for the new sequential G.O.F. test procedure have been generated. Using the critical values and significance levels, a sequential G.O. F. test procedure can be used to determine if the given sample data agrees with a hypothesized Weibull distribution with known shape. A power study has been conducted against a variety of alternative hypotheses, and the results were compared with those obtained using conventional EDF type Cramer-von Mises, Ahderson-Darling and Kolmogorov-Smimov G.O.F tests, and the sequential procedure by Clough. Since the sequential test demonstrates better or equivalent power, it serves to significantly reduce the computational requirements for powerful G.O. F. testing.

Modified Goodness Of Fit Tests For The Weibull Distribution

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Author :
language : en
Publisher:
Release Date : 1993

Modified Goodness Of Fit Tests For The Weibull Distribution written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.

This research will produce a new modified Anderson-Darling and W* goodness of fit statistics for the three parameter Weibull Distribution when all parameters unknown and estimated by Maximum Likelihood-Minimum Distance combination. The critical values for each statistic, sample size and a levels 0. 20, 0.15, 0.10, 0.05 and 0.01 are produced. The Monte Carlo Simulation used 5000 repetitions for sample sizes of 10, 15, 20, 25, 30, 40, and 50 with the Weibull shape equals to 3, scale equals to 4 and location equals to 10. The power study is made for the same sizes as above with the hypothesized Weibull Distribution against 8 other distributions ... Weibull distribution, Goodness-of-fitness, Monte Carlo simulation, Minimum distance, Maximum likelihood.

A Comparison Of Classification And Hypothesis Testing Procedures For Choosing Between Competing Families Of Distributions Including A Survey Of The Goodness Of Fit Tests

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Author : Alan R. Dyer
language : en
Publisher:
Release Date : 1971

A Comparison Of Classification And Hypothesis Testing Procedures For Choosing Between Competing Families Of Distributions Including A Survey Of The Goodness Of Fit Tests written by Alan R. Dyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.

Procedures for determining from which of two parametric families a random sample has been drawn are considered. Primary attention is focused on families which are location and/or scale invariant. The procedures are compared using Monte Carlo sampling techniques for six pairs of distributions. Certain procedures based on sample spacing are shown to compare quite favorably with the 'best' invariant and likelihood ratio procedures. Procedures are considered in both the classification and hypothesis testing frameworks. (Author).

A New Goodness Of Fit Test For The Weibull Distribution Based On Spacings

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