{"title":"Estimation of Parameters of Misclassified Size Biased Uniform Poisson Distribution and Its Application","authors":"B. S. Trivedi, D. R. Barot, M. N. Patel","doi":"10.3103/s106653072470008x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Statistical data analysis is of great interest in every field of\nmanagement, business, engineering, medicine, etc. At the time of\nclassification and analysis, errors may arise, like a\nclassification of observation in the other class instead of the\nactual class. All fields of science and economics have substantial\nproblems due to misclassification errors in the observed data. Due\nto a misclassification error in the data, the sampling process may\nnot suggest an appropriate probability distribution, and in that\ncase, inference is impaired. When these types of errors are\nidentified in variables, it is expected to consider the problem’s\nsolution regarding classification errors. This paper presents the\nsituation where specific counts are reported erroneously as\nbelonging to other counts in the context of size biased Uniform\nPoisson distribution, the so-called misclassified size biased\nUniform Poisson distribution. Further, we have estimated the\nparameters of misclassified size biased Uniform Poisson\ndistribution by applying the method of moments, maximum likelihood\nmethod, and approximate Bayes estimation method. A simulation\nstudy is carried out to assess the performance of estimation\nmethods. A real dataset is discussed to demonstrate the\nsuitability and applicability of the proposed distribution in the\nmodeling count dataset. A Monte Carlo simulation study is\npresented to compare the estimators. The simulation results show\nthat the ML estimates perform better than their corresponding\nmoment estimates and approximate Bayes estimates.</p>","PeriodicalId":46039,"journal":{"name":"Mathematical Methods of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s106653072470008x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Statistical data analysis is of great interest in every field of
management, business, engineering, medicine, etc. At the time of
classification and analysis, errors may arise, like a
classification of observation in the other class instead of the
actual class. All fields of science and economics have substantial
problems due to misclassification errors in the observed data. Due
to a misclassification error in the data, the sampling process may
not suggest an appropriate probability distribution, and in that
case, inference is impaired. When these types of errors are
identified in variables, it is expected to consider the problem’s
solution regarding classification errors. This paper presents the
situation where specific counts are reported erroneously as
belonging to other counts in the context of size biased Uniform
Poisson distribution, the so-called misclassified size biased
Uniform Poisson distribution. Further, we have estimated the
parameters of misclassified size biased Uniform Poisson
distribution by applying the method of moments, maximum likelihood
method, and approximate Bayes estimation method. A simulation
study is carried out to assess the performance of estimation
methods. A real dataset is discussed to demonstrate the
suitability and applicability of the proposed distribution in the
modeling count dataset. A Monte Carlo simulation study is
presented to compare the estimators. The simulation results show
that the ML estimates perform better than their corresponding
moment estimates and approximate Bayes estimates.
期刊介绍：
Mathematical Methods of Statistics is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.
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