Research on Complex Equipment Reliability Growth AMSAA-ELP Model Based on Explore Learning Promotion

2014 ◽  
Vol 940 ◽  
pp. 531-534 ◽  
Author(s):  
Na Zhang
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Trend Test ◽  
Reliability Growth ◽  
Goodness Of Fit Test ◽  
Model Based ◽  
Estimation Formula ◽  
Equipment Reliability ◽  
Complex Equipment

According to learning other models equipment test information of complex equipment in the development process, and making their own systems to improve the reliability of the case, a complex equipment reliability growth AMSAA-ELP model based on explore learning promotion was developed, and the property was analyzed from different parameter values. Additionally, the trend test was also presented. Secondly, maximum likelihood estimation formula of the parameters was given under time censored and failure censored test of AMSAA-ELP model, and point out that there are multiple poles value of the maximum likelihood estimate can use pseudo-Monte-Carlo method parameter calculation. Additionally, the model's goodness of fit test was also given. Finally, the combination of complex equipment with engine failure data was analyzed. The results shows that the AMSAA-ELP model is prefer to AMSAA model intended to test data, and the AMSAA-ELP model is suitable to the engineering applications.

scholarly journals Maximum Likelihood Estimation for the Generalized Pareto Distribution and Goodness-of-Fit Test with Censored Data

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Minh H. Pham ◽  
Chris Tsokos ◽  
Bong-Jin Choi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Censored Data ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Likelihood Estimation ◽  
R Package ◽  
Goodness Of Fit Test ◽  
Generalized Pareto

The generalized Pareto distribution (GPD) is a flexible parametric model commonly used in financial modeling. Maximum likelihood estimation (MLE) of the GPD was proposed by Grimshaw (1993). Maximum likelihood estimation of the GPD for censored data is developed, and a goodness-of-fit test is constructed to verify an MLE algorithm in R and to support the model-validation step. The algorithms were composed in R. Grimshaw’s algorithm outperforms functions available in the R package ‘gPdtest’. A simulation study showed the MLE method for censored data and the goodness-of-fit test are both reliable.

scholarly journals Modelling the number of olive groves in Spanish municipalities

2016 ◽  
Vol 14 (1) ◽  
pp. e0201
Author(s):  
Maria-Dolores Huete ◽  
Juan A. Marmolejo
Keyword(s):  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
External Factors ◽  
Discrete Distributions ◽  
Future Research ◽  
Total Output ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Total Variability ◽  
Olive Groves

<p>The univariate generalized Waring distribution (UGWD) is presented as a new model to describe the goodness of fit, applicable in the context of agriculture. In this paper, it was used to model the number of olive groves recorded in Spain in the 8,091 municipalities recorded in the 2009 Agricultural Census, according to which the production of oil olives accounted for 94% of total output, while that of table olives represented 6% (with an average of 44.84 and 4.06 holdings per Spanish municipality, respectively). UGWD is suitable for fitting this type of discrete data, with strong left-sided asymmetry. This novel use of UGWD can provide the foundation for future research in agriculture, with the advantage over other discrete distributions that enables the analyst to split the variance. After defining the distribution, we analysed various methods for fitting the parameters associated with it, namely estimation by maximum likelihood, estimation by the method of moments and a variant of the latter, estimation by the method of frequencies and moments. For oil olives, the chi-square goodness of fit test gives <em>p</em>-values of 0.9992, 0.9967 and 0.9977, respectively. However, a poor fit was obtained for the table olive distribution. Finally, the variance was split, following Irwin, into three components related to random factors, external factors and internal differences. For the distribution of the number of olive grove holdings, this splitting showed that random and external factors only account about 0.22% and 0.05%. Therefore, internal differences within municipalities play an important role in determining total variability.</p>

scholarly journals Asymptotic Distribution of Cramer-von Mises Statistic When Contamination Exists

2015 ◽  
Vol 5 (1) ◽  
pp. 90
Author(s):  
Mayumi Naka ◽  
Ritei Shibata
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Distribution ◽  
Minimum Distance ◽  
Goodness Of Fit ◽  
Likelihood Estimator ◽  
Goodness Of Fit Test ◽  
Minimum Distance Estimator ◽  
Von Mises Statistic ◽  
Von Mises ◽  
Distance Estimator

In this paper, asymptotic distribution of Cram\'er-von Mises goodness-of-fit test statistic is investigated when contamination exists.<br />We first derive the asymptotic distribution of the Cram\'er-von Mises statistic when the observations are contaminated with noise as a mixture.<br />The result is extended to the case where the parameters are estimated by the minimum distance estimator,<br />which minimizes the Cram\'er-von Mises statistic.<br />In both cases the asymptotic distribution of the Cram\'er-von Mises statistic is given by that of the weighted infinite sum of non-central $\chi^2_1$ variables and the effect of contamination appears only in the non-centrality of the variables.<br />We also demonstrate the robustness of the goodness-of-fit test by Monte Carlo simulations when the parameters are estimated<br />by the minimum distance estimator and the maximum likelihood estimator.<br />Numerical experiments indicate that the use of the minimum distance estimator makes the test insensitive to contamination whereas the power is retained almost the same as that of the maximum likelihood estimator.

scholarly journals Multivariate Hawkes processes: an application to financial data

2011 ◽  
Vol 48 (A) ◽  
pp. 367-378 ◽  
Author(s):  
Paul Embrechts ◽  
Thomas Liniger ◽  
Lu Lin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Estimation ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Financial Data ◽  
Data Sets ◽  
Hawkes Process ◽  
Science And Engineering ◽  
Hawkes Processes

A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

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.

Fitting The Best–Fit Distribution For The Hourly Rainfall Amount In The Wilayah Persekutuan

2012 ◽  
Author(s):  
Fadhilah Y. ◽  
Zalina Md. ◽  
Nguyen V–T–V. ◽  
Suhaila S. ◽  
Zulkifli Y.
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Rainfall Amount ◽  
Likelihood Method ◽  
Exceedance Probability ◽  
Parameter Estimates ◽  
Goodness Of Fit Test ◽  
Hourly Rainfall ◽  
Best Fit ◽  
Mixed Exponential Distribution

Dalam mengenal pasti model yang terbaik untuk mewakili taburan jumlah hujan bagi data selang masa satu jam di 12 stesen di Wilayah Persekutuan empat taburan digunakan iaitu Taburan Eksponen, Gamma, Weibull dan Gabungan Eksponen. Parameter–parameter dianggar menggunakan kaedah kebolehjadian maksimum. Model yang terbaik dipilih berdasarkan nilai minimum yang diperolehi daripada ujian–ujian kebagusan penyuaian yang digunakan dalam kajian ini. Ujian ini dipertahankan lagi dengan plot kebarangkalian dilampaui. Taburan Gabungan Eksponen di dapati paling baik untuk mewakili taburan jumlah hujan dalam selang masa satu jam. Daripada anggaran parameter bagi taburan Gabungan Eksponen ini, boleh diterjemah bahawa jumlah hujan tertinggi yang direkodkan diperolehi daripada hujan yang dikategorikan sebagai hujan lebat, walaupun hujan renyai–renyai berlaku lebih kerap. Kata kunci: Jumlah hujan dalam selang masa sejam, ujian kebagusan penyuaian, kebolehjadian maksimum In determining the best–fit model for the hourly rainfall amounts for the twelve stations in the Wilayah Persekutuan, four distributions namely, the Exponential, Gamma, Weibull and Mixed–Exponential were used. Parameters for each distribution were estimated using the maximum likelihood method. The best–fit model was chosen based upon the minimum error produced by the goodness–offit tests used in this study. The tests were justified further by the exceedance probability plot. The Mixed–Exponential was found to be the most appropriate distribution in describing the hourly rainfall amounts. From the parameter estimates for the Mixed–Exponential distribution, it could be implied that most of the hourly rainfall amount recorded were received from the heavy rainfall even though there was a high occurrences of light rainfall. Key words: Hourly rainfall amount, goodness-of-fit test, exceedance probability, maximum likelihood

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