A New Goodness-of-Fit Test for the Two-Parameter Gamma Distribution

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.

Some Classes of Logarithmic-Type Imputation Techniques for Handling Missing Data

In this manuscript, three new classes of log-type imputation techniques have been proposed to handle missing data when conducting surveys. The corresponding classes of point estimators have been derived for estimating the population mean. Their properties (Mean Square Errors and bias) have been studied. An extensive simulation study using data generated from normal, Poisson, and Gamma distributions, as well as real dataset, has been conducted to evaluate how the proposed estimator performs in comparison to several contemporary estimators. The results have been summarized, and discussion regarding real-life applications of the estimator follows.

Confidence Intervals for the Ratio of the Coefficients of Variation of Inverse-Gamma Distributions

Herein, we present four methods for constructing confidence intervals for the ratio of the coefficients of variation of inverse-gamma distributions using the percentile bootstrap, fiducial quantities, and Bayesian methods based on the Jeffreys and uniform priors. We compared their performances using coverage probabilities and expected lengths via simulation studies. The results show that the confidence intervals constructed with the Bayesian method based on the uniform prior and fiducial quantities performed better than those constructed with the Bayesian method based on the Jeffreys prior and the percentile bootstrap. Rainfall data from Thailand was used to illustrate the efficacies of the proposed methods.

Relationship among Continuous Probability Distributions and Interpolation

Aims: The Study seeks to determine the relationship that exists among Continuous Probability Distributions and the use of Interpolation Techniques to estimate unavailable but desired value of a given probability distribution. Study Design: Statistical Probability tables for Normal, Student t, Chi-squared, F and Gamma distributions were used to compare interpolated values with statistical tabulated values. Charts and Tables were used to represent the relationships among the five probability distributions. Methodology: Linear Interpolation Technique was employed to interpolate unavailable but desired values so as to obtain approximate values from the statistical tables. The data were analyzed for interpolation of unavailable but desired values at 95% a-level from the five continuous probability distribution. Results: Interpolated values are as close as possible to the exact values and the difference between the exact value and the interpolated value is not pronounced. The table and chart established showed that relationships do exist among the Normal, Student-t, Chi-squared, F and Gamma distributions. Conclusion: Interpolation techniques can be applied to obtain unavailable but desired information in a data set. Thus, uncertainty found in a data set can be discovered, then analyzed and interpreted to produce desired results. However, understanding of how these probability distributions are related to each other can inform how best these distributions can be used interchangeably by Statisticians and other Researchers who apply statistical methods employed in practical applications.

Comparison of parametric and semi-parametric models with randomly right-censored data by weighted estimators: Two applications in colon cancer and hepatocellular carcinoma datasets

In this study, parametric and semi-parametric regression models are examined for random right censorship. The components of the aforementioned regression models are estimated with weights based on Cox and Kaplan–Meier estimates, which are semi-parametric and nonparametric methods used in survival analysis, respectively. The Tobit based on weights obtained from a Cox regression is handled as a parametric model instead of other parametric models requiring distribution assumptions such as exponential, Weibull, and gamma distributions. Also, the semi-parametric smoothing spline and the semi-parametric smoothing kernel estimators based on Kaplan–Meier weights are used. Therefore, estimates are obtained from two models with flexible approaches. To show the flexible shape of the models depending on the weights, Monte Carlo simulations are conducted, and all results are presented and discussed. Two empirical datasets are used to show the performance of the aforementioned estimators. Although three approaches gave similar results to each other, the semi-parametric approach was slightly superior to the parametric approach. The parametric approach method, on the other hand, yields good results in medium and large sample sizes and at a high censorship level. All other findings have been shared and interpreted.

An Exponential-Cum-Sine-Type Hybrid Imputation Technique for Missing Data

In this study, a new exponential-cum-sine-type hybrid imputation technique has been proposed to handle missing data when conducting surveys. The properties of the corresponding point estimator for population mean have been examined in terms of bias and mean square errors. An extensive simulation study using data generated from normal, Poisson, and Gamma distributions has been conducted to evaluate how the proposed estimator performs in comparison to several contemporary estimators. The results have been summarized, and discussion regarding real-life applications of the estimator follows.

Random Variables

Specializing the concepts of Chapter 7 to the case of real variables, this chapter introduces distribution functions, discrete and continuous distributions, and describes examples such as the binomial, uniform, Gaussian, Cauchy, and gamma distributions. It then treats multivariate distributions and the concept of independence.

A Notable Bounded Probability Distribution for Environmental and Lifetime Data

In this article, we introduce a notable bounded distribution based on a modification of the epsilon function which creates an upper bound on the domain of the distribution. Further, a key feature of the distribution links the readers with the asymptotic connections with the famous Lindley distribution, which is a weighted variant of the exponential distribution and also a mixture of exponential and gamma distributions. In some ways, the proposed distribution provides a flexible solution to the modeling of bounded characteristics that can be almost well-fitted by the Lindley distribution if the domain is restricted. Moreover, we have also explored its application, particularly with reference to lifetime and environmental points of view, and found that the proposed model exhibits a better fit among the competing models. Further, from the annual rainfall analysis, the proposed model exhibits a realistic return period of the rainfall.