Estimation of Parameters of Misclassified Size Biased Uniform Poisson Distribution and Its Application

IF 0.8 Q3 STATISTICS & PROBABILITY Mathematical Methods of Statistics Pub Date : 2024-07-15 DOI:10.3103/s106653072470008x

B. S. Trivedi, D. R. Barot, M. N. Patel

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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.

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误分类大小偏差均匀泊松分布参数估计及其应用

摘要统计数据分析在管理、商业、工程、医学等各个领域都具有重要意义。在进行分类和分析时，可能会出现错误，如将观测数据归入其他类别而非实际类别。科学和经济学的所有领域都存在因观测数据分类错误而导致的重大问题。由于数据中的分类错误，抽样过程可能无法显示适当的概率分布，在这种情况下，推断就会受到影响。当发现变量中存在这类误差时，就需要考虑如何解决分类误差问题。本文介绍了在大小偏统一泊松分布的背景下，特定计数被错误地报告为属于其他计数的情况，即所谓的误分类大小偏统一泊松分布。此外，我们还运用矩量法、最大似然法和近似贝叶斯估计法估计了误分类大小偏倚均匀泊松分布的参数。通过模拟研究来评估估计方法的性能。讨论了一个真实数据集，以证明所提出的分布在模拟计数数据集中的适用性和应用性。为了比较估计方法，还进行了蒙特卡罗模拟研究。仿真结果表明，ML 估计结果优于相应的矩估计结果和近似贝叶斯估计结果。

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来源期刊

Mathematical Methods of Statistics STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

0.00%

发文量

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.