scholarly journals Smooth Tests of Fit for the Lindley Distribution

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 92-97
Author(s):  
D. Best ◽  
J. Rayner
Keyword(s):  
Exponential Distribution ◽  
Lindley Distribution ◽  
Smooth Tests ◽  
Smooth Test ◽  
Anderson Darling ◽  
Tests Of Fit

We consider the little-known one parameter Lindley distribution. This distribution may be of interest as it appears to be more flexible than the exponential distribution, the Lindley fitting more data than the exponential. We give smooth tests of fit for this distribution. The smooth test for the Lindley has power comparable with the Anderson-Darling test. Advantages of the smooth test are discussed. Examples that illustrate the flexibility of this distributions is given.

scholarly journals Tests of Fit for the Logarithmic Distribution

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
D. J. Best ◽  
J. C. W. Rayner ◽  
O. Thas
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Probability Generating Function ◽  
Smooth Tests ◽  
The Third ◽  
Chi Squared ◽  
Logarithmic Distribution ◽  
Anderson Darling ◽  
Tests Of Fit ◽  
Integrated Distribution Function

Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists.

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

scholarly journals Informational Energy and Entropy Applied to Testing Exponentiality

2020 ◽  
Vol 8 (1) ◽  
pp. 220-228
Author(s):  
Hadi Alizadeh Noughabi ◽  
Havva Alizadeh Noughabi ◽  
Jalil Jarrahiferiz
Keyword(s):  
Exponential Distribution ◽  
Simulation Study ◽  
Waiting Times ◽  
Critical Values ◽  
Life Testing ◽  
Time Between Failures ◽  
The Usa ◽  
Informational Energy ◽  
Tests Of Fit

The exponential distribution is widely used in reliability and life testing analysis. In this paper, two tests of fit for the exponential distribution based on Informational Energy and entropy are constructed. Consistency and other properties of the tests are proved. Using a simulation study, critical values of the proposed tests are obtained and then power values of tests are computed and compared with each other against various alternatives. Finally, we apply the tests for time between failures of secondary reactor pumps and waiting times for fatal plane accidents in the USA from 1983 to 1998.

scholarly journals Characterizations of Twenty (2020-2021) Proposed Discrete Distributions

2021 ◽  
pp. 847-884
Author(s):  
G.G. Hamedani ◽  
Mahrokh Najaf ◽  
Amin Roshani ◽  
Nadeem Shafique Butt
Keyword(s):  
Exponential Distribution ◽  
Poisson Distribution ◽  
Geometric Distribution ◽  
Discrete Distribution ◽  
Gumbel Distribution ◽  
Rayleigh Distribution ◽  
Discrete Distributions ◽  
Lindley Distribution ◽  
Lomax Distribution ◽  
Two Parameter

In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete gen- eralized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distri- bution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Fr¨uhwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall–Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the au- thors’ works.

Do Suicides From the Golden Gate Bridge Cluster?

2016 ◽  
Vol 118 (1) ◽  
pp. 70-73
Author(s):  
Donald W. Mackenzie ◽  
David Lester ◽  
Russell Manson ◽  
Cynthia Yeh
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Null Hypothesis ◽  
Golden Gate ◽  
Negative Exponential Distribution ◽  
Anderson Darling ◽  
Clustering Data ◽  
Golden Gate Bridge ◽  
Negative Exponential ◽  
Over Time

Suicides from popular venues (known as “hotspots”) are often publicized and may result in imitation by subsequent suicides that may lead to clustering of the suicides over time. In order to examine whether the suicides from the Golden Gate Bridge showed clustering, data from the 224 suicides during 1999–2009 were analyzed using the Anderson-Darling Test was run on the data against a null hypothesis of a negative exponential distribution (as would be generated by a homogenous Poisson process). It was found that the data were almost a perfect fit for the Poisson distribution and so showed no evidence of clustering beyond that expected to occur by chance alone. This indicates that there was no imitation or contagion in the suicides from the Golden Gate Bridge.

scholarly journals A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 135 ◽  
Author(s):  
Ahmed Z. Afify ◽  
Osama Abdo Mohamed
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

The Missing Tail and Other Considerations for the Use of Fire History Models

1995 ◽  
Vol 5 (4) ◽  
pp. 197 ◽  
Author(s):  
MA Finney
Keyword(s):  
Exponential Distribution ◽  
Exponential Model ◽  
Forest Age ◽  
Age Classes ◽  
Class Distribution ◽  
Age Class ◽  
Negative Exponential Distribution ◽  
Negative Exponential Model ◽  
Negative Exponential ◽  
Tests Of Fit

This paper reviews methods used for testing the fit of the cumulative form of a negative exponential distribution to the cumulative distribution of forest age-classes. It is shown that existing methods can lead to a greater chance of falsely rejecting the fit of the negative exponential model and inferring that fire frequencies have changed through time. This results when the old-age tail of a negative exponential distribution is mathematically assumed to be present at the end of the age-class distribution. In reality, the tail is censored from sample distributions of forest age-classes. Censoring alters the shape of a cumulative age-class distribution from the straight line expected for a semi-log graph of the cumulative negative exponential model. A solution to this problem is proposed that restricts the tests-of-fit to the portion of the negative exponential distribution that overlaps with the data to be tested. The cumulative age-class distribution can then be compared directly with the cumulative of a truncated negative exponential distribution. Considerations for interpreting a poor fit are then discussed.

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