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In this article, a novel bounded interval model called the unit‐Perks model is developed by suitably transforming the positive random variable of the Perks distribution. Numerous statistical features of the bounded interval Perks model are being explored based on the expansion of the density function. Eight distinct estimation approaches are being used to estimate the parameters of the unit‐Perks model. A throughout simulation analysis is also included to evaluate the precision of the resulting estimators from eight estimating approaches. Two real bounded interval data sets are being utilized to investigate the practical applicability of the unit‐Perks model. A comparison is also made to determine which method of estimation works better for the given model. According to a comparison of eight different estimation approaches, the maximum likelihood estimation approach outperformed than the other seven estimating approaches. The unit‐perks model is then used to introduce the quantile regression model named as quantile unit‐Perks distribution. Application to real data set for the quantile unit‐Perks distribution is also performed. The quantile residuals are used for the residual analysis of the fitted regression model. On the basis of mathematical, computational, and pictorial evidences, it is concluded that the presented model exhibited greater modeling capabilities. [ABSTRACT FROM AUTHOR]

The generalized Gamma distribution is widely used in survival analysis, engineering and economics, and it includes the Gamma distribution as a special case. In real life applications, the Generalized Gamma distribution may be an unnecessarily complicated distribution to fit when one of the simpler models may be sufficient to analyze the data. The aim of this paper is to develop tests of goodness of fit of the two parameter gamma distribution against its three parameter counterpart. Specifically, we develop Wald, C (α) , score, likelihood ratio, and gradient tests. These tests are then compared in terms of empirical size and power using a simulation study. [ABSTRACT FROM AUTHOR]

This paper presents the results of the statistical modeling of the ozone concentration in Campo Grande, Brazil in 2016. Five sets of data, summer (January–March), autumn (April–June), winter (July–September), spring (October–December), and all year round were used. The results show that the maximum concentrations of oxidants occur at 3:00 p.m., the diurnal NO variation, the concentrations show a cycle with two peaks at 7:00 and the other at 11:00 p.m. It has been found that the best distribution for the five datasets is the lognormal distribution of three parameters. The seasonality of the datasets shows greater asymmetry during the summer, due to the greater tail distribution, mainly due to the greater photochemical activity. [ABSTRACT FROM AUTHOR]

Nonparametric tests are useful when underlying distribution of a population is unknown or sample size is quiet small to satisfy assumptions of a traditional F test. Nonparametric tests have a good usage in a sample which consists of observations from various populations, as well. Randomized block designs are purposive when experimental subjects vary in natural heterogeneity. Nonparametric tests which are suitable for two-way ANOVA designs where the blocks containing observations which follow an increasing or a decreasing trend are main focus of this study. A recently proposed nonparametric test which was developed as an alternative to Jonckheere test is modified for ordered alternative hypotheses in randomized complete block designs. This modification test and several nonparametric tests for detecting ordered alternative hypotheses in randomized complete block designs are compared empirically in a broad set of Monte Carlo simulations under different conditions. A numerical example is provided to illustrate test procedures. The modified test provides better performance than Jonckheere test in terms of type I error and power values whereas Hollander test provides slightly better power values among the other test statistics. In terms of type I error values, it can be stated that the most conservative test is Jonckheere test whereas, estimated type 1 error values of the other test statistics are usually closer to nominal level of alpha. [ABSTRACT FROM AUTHOR]

Count data consists of discrete non-negative integer values. Poisson regression model is one of the most popular model used to model count data. This model assumes that response variable has Poisson distribution. The purpose of this article is to assess distributional assumption of this model by using some goodness of fit tests. These tests are compared in respect to type I error and power rates of tests with different samples, parameters and sample sizes. Simulation study suggests that the most powerful tests are generally Dean-Lawless and Cameron-Trivedi score tests. [ABSTRACT FROM AUTHOR]