scholarly journals A Modified Chi-square Type Test for Distributional Validity with Applications to Right Censored Reliability and Medical Data

2021 ◽  
pp. 1113-1121 ◽  
Author(s):  
Haitham M. Yousof ◽  
Abdullah H. Al-nefaie ◽  
Khaoula Aidi ◽  
M. Masoom Ali ◽  
Mohamed ibrahim Mohamed
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
Type Test ◽  
The Right ◽  
New Distribution

In this paper, a modified Chi-square goodness-of-fit test called the modified Bagdonavičius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored Barzilai-Borwein is employed via a comprehensive simulation study for assessing validity of the new test. The modified Bagdonavičius-Nikulin test is applied to four real and right censored data sets. A new distribution is compared with many other competitive distributions under the new modified Bagdonavičius-Nikulin goodness-of-fit test statistic.

scholarly journals A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data

2021 ◽  
pp. 615-623
Author(s):  
Khaoula Aidi ◽  
Nadeem Shafique Butt ◽  
Mir Masoom Ali ◽  
Mohamed Ibrahim ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Right Censored Data ◽  
The Right

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

scholarly journals A new parametric lifetime model with modified chi-square type test for right censored validation, characterizations and different estimation methods

2021 ◽  
pp. 399-425
Author(s):  
Haitham Yousof ◽  
Khaoula Aidi ◽  
G.G. Hamedani ◽  
Mohamed Ibrahim
Keyword(s):  
Censored Data ◽  
Goodness Of Fit ◽  
Real Data ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Data Set ◽  
Right Censored Data ◽  
New Model ◽  
The Right

A new three-parameter extension of the generalized Nadarajah-Haghighi model is introduced and studied. Some of its statistical properties are derived. Characterization results are presented. The failure rate can be "increasing", "decreasing", "bathtub", "upside-down", "upside-down-constant", "increasing-constant" or "constant". Different non-Bayesian estimation methods under uncensored scheme are considered. Numerical simulations are performed for comparing the estimation methods using different sample sizes. The censored Barzilai-Borwein algorithm is employed via a simulation study. Using the approach of the Bagdonavicius-Nikulin chi-square goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. Based on the maximum likelihood estimators on initial data, the modified Bagdonavicius-Nikulin chi-square goodness-of-fit test recovers the loss in information. The modified Bagdonavicius-Nikulin test for validation under the right censored data is applied to four real and right censored data sets. The new model is compared with many other competitive models by means of a real data set.

scholarly journals Testing in Nonparametric Accelerated Life Time Models

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Hannelore Liero
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Bootstrap Method ◽  
Life Time ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Time Model ◽  
Power Of The Test ◽  
Accelerated Life ◽  
Type Test

A goodness-of-fit test for testing the acceleration function in a nonparametric life time model is proposed. For this aim the limit distribution of an L2-type test statistic is derived. Furthermore, a bootstrap method is considered and the power of the test is studied.

scholarly journals A Least Squares Estimation Method for the Linear Learning Model

1978 ◽  
Vol 15 (1) ◽  
pp. 145-153
Author(s):  
Berend Wierenga
Keyword(s):  
Least Squares ◽  
Simulation Study ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Estimation Method ◽  
Learning Model ◽  
New Method ◽  
Data Sets ◽  
Goodness Of Fit Test ◽  
Chi Square

The author presents a new method for estimating the parameters of the linear learning model. The procedure, essentially a least squares method, is easy to carry out and avoids certain difficulties of earlier estimation procedures. Applications to three different data sets are reported, as well as results from a goodness-of-fit test. A simulation study was carried out to validate the method. The outcomes are compared with those obtained from the minimum chi square estimation method. The results of the new method appear to be satisfactory.

scholarly journals Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1949
Author(s):  
Mukhtar M. Salah ◽  
M. El-Morshedy ◽  
M. S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Least Square Estimation ◽  
Chi Square ◽  
Anderson Darling ◽  
The Right

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given.

scholarly journals Validation of the Odd Lindley Exponentiated Exponential by a ModiÖed Goodness of Fit Test with Applications to Censored and Complete Data

2019 ◽  
pp. 745-771 ◽  
Author(s):  
Hafida Goual ◽  
Haitham M. Yousof ◽  
Mir Masoom Ali
Keyword(s):  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Complete Data ◽  
Data Sets ◽  
Grouped Data ◽  
Goodness Of Fit Test ◽  
Right Censored Data ◽  
Mathematical Properties ◽  
Chi Squared

In this paper, we Örst introduse a new extension of the exponentiated exponential distribution along with its several mathematical properties. Second, we construct a modiÖed Chi-squared goodness-of-Öt test based on the Nikulin-Rao-Robson statistic in presence of censored and complete data. We describe the theory and the mechanism of the Y 2 n statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various Öelds, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other right censored data sets.

scholarly journals Evaluating Rank Histograms Using Decompositions of the Chi-Square Test Statistic

2008 ◽  
Vol 136 (6) ◽  
pp. 2133-2139 ◽  
Author(s):  
Ian T. Jolliffe ◽  
Cristina Primo
Keyword(s):  
Goodness Of Fit ◽  
Ensemble Forecasting ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Chi Square Test ◽  
Forecasting System ◽  
Rank Histogram ◽  
Von Mises ◽  
Cramer Von Mises

Abstract Rank histograms are often plotted to evaluate the forecasts produced by an ensemble forecasting system—an ideal rank histogram is “flat” or uniform. It has been noted previously that the obvious test of “flatness,” the well-known χ2 goodness-of-fit test, spreads its power thinly and hence is not good at detecting specific alternatives to flatness, such as bias or over- or underdispersion. Members of the Cramér–von Mises family of tests do much better in this respect. An alternative to using the Cramér–von Mises family is to decompose the χ2 test statistic into components that correspond to specific alternatives. This approach is described in the present paper. It is arguably easier to use and more flexible than the Cramér–von Mises family of tests, and does at least as well as it in detecting alternatives corresponding to bias and over- or underdispersion.

scholarly journals A New Parametric Life Distribution with Modified Bagdonavičius–Nikulin Goodness-of-Fit Test for Censored Validation, Properties, Applications, and Different Estimation Methods

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 592 ◽  
Author(s):  
Mahmoud Mansour ◽  
Mahdi Rasekhi ◽  
Mohamed Ibrahim ◽  
Khaoula Aidi ◽  
Haitham M. Yousof ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Real Data ◽  
Weibull Model ◽  
Estimation Methods ◽  
Model Parameters ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Data Set ◽  
The Right

In this paper, we first study a new two parameter lifetime distribution. This distribution includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.

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