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Register a new userPower Maxwell distribution: Statistical Properties, Estimation and Application
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Added by
Dr Abhimanyu Singh Yadav
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure rate. Different statistical properties such as reliability characteristics, moments, quantiles, mean deviation, generating function, conditional moments, stochastic ordering, residual lifetime function and various entropy measures have been derived. The estimation of the parameters for the proposed probability distribution has been addressed by maximum likelihood estimation method and Bayes estimation method. The Bayes estimates are obtained under gamma prior using squared error loss function. Lastly, real-life application for the proposed distribution has been illustrated through different lifetime data.
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This paper proposed a new probability distribution named as inverse xgamma distribution (IXGD). Different mathematical and statistical properties,viz., reliability characteristics, moments, inverse moments, stochastic ordering and order statistics of the proposed distribution have been derived and discussed. The estimation of the parameter of IXGD has been approached by different methods of estimation, namely, maximum likelihood method of estimation (MLE), Least square method of estimation (LSE), Weighted least square method of estimation (WLSE), Cramer-von-Mises method of estimation (CME) and maximum product spacing method of estimation (MPSE). Asymptotic confidence interval (ACI) of the parameter is also obtained. A simulation study has been carried out to compare the performance of the obtained estimators and corresponding ACI in terms of average widths and corresponding coverage probabilities. Finally, two real data sets have been used to demonstrate the applicability of IXGD in real life situations.
This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of the statistical inference methodology and to utilize distribution estimators in practice. We also include in the discussion the topic of generalized fiducial inference, a special type of modern distributional inference, and relate it to the concept of confidence distribution. Several real data examples are also provided for practitioners. We hope that the selected content covers the greater part of the developments on this subject.
During the last few decades, online controlled experiments (also known as A/B tests) have been adopted as a golden standard for measuring business improvements in industry. In our company, there are more than a billion users participating in thousands of experiments simultaneously, and with statistical inference and estimations conducted to thousands of online metrics in those experiments routinely, computational costs would become a large concern. In this paper we propose a novel algorithm for estimating the covariance of online metrics, which introduces more flexibility to the trade-off between computational costs and precision in covariance estimation. This covariance estimation method reduces computational cost of metric calculation in large-scale setting, which facilitates further application in both online controlled experiments and adaptive experiments scenarios like variance reduction, continuous monitoring, Bayesian optimization, etc., and it can be easily implemented in engineering practice.
Entity resolution identifies and removes duplicate entities in large, noisy databases and has grown in both usage and new developments as a result of increased data availability. Nevertheless, entity resolution has tradeoffs regarding assumptions of the data generation process, error rates, and computational scalability that make it a difficult task for real applications. In this paper, we focus on a related problem of unique entity estimation, which is the task of estimating the unique number of entities and associated standard errors in a data set with duplicate entities. Unique entity estimation shares many fundamental challenges of entity resolution, namely, that the computational cost of all-to-all entity comparisons is intractable for large databases. To circumvent this computational barrier, we propose an efficient (near-linear time) estimation algorithm based on locality sensitive hashing. Our estimator, under realistic assumptions, is unbiased and has provably low variance compared to existing random sampling based approaches. In addition, we empirically show its superiority over the state-of-the-art estimators on three real applications. The motivation for our work is to derive an accurate estimate of the documented, identifiable deaths in the ongoing Syrian conflict. Our methodology, when applied to the Syrian data set, provides an estimate of $191,874 pm 1772$ documented, identifiable deaths, which is very close to the Human Rights Data Analysis Group (HRDAG) estimate of 191,369. Our work provides an example of challenges and efforts involved in solving a real, noisy challenging problem where modeling assumptions may not hold.
This article aims to introduced a new lifetime distribution named as exponentiated xgamma distribution (EXGD). The new generalization obtained from xgamma distribution, a special finite mixture of exponential and gamma distributions. The proposed model is very flexible and positively skewed. Different statistical properties of the proposed model, viz., reliability characteristics, moments, generating function, mean deviation, quantile function, conditional moments, order statistics, reliability curves and indices and random variate generation etc. have been derived. The estimation of the of the survival and hazard rate functions of the EXGD has been approached by different methods estimation, viz., moment estimate (ME),maximum likelihood estimate (MLE), ordinary least square and weighted least square estimates (LSE and WLSE), Cram`er-von-Mises estimate (CME) and maximum product spacing estimate (MPSE). At last, one medical data set has been used to illustrate the applicability of the proposed model in real life scenario.
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