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.

Behaviour of spatial rainfall correlation For short distances

The correlation between two series of rainfall recorded at two stations which are at short distance, is usually found significant. This information has important applicability in the areas of data interpolation, network design, transfer of information in respect of missing data and deriving areal rainfall from point values. In this paper 70-year (1901-1970) annual rainfall data for about 1500 stations in India have been analysed. The distribution of correlation coefficient (r) for the stations located within a distance of 40 km were obtained. Attempt has been made to derive theoretical model of r. For this purpose two distributions, (1) a two parameter -distribution and (2) a two parameter bounded distribution, have been chosen as in both cases the variable ranges from 0 to 1.

An Inferential Aptness of a Weibull Generated Distribution and Application

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

A kriging-based analysis of cloud Liquid Water Content using CloudSat data

Spatiotemporal statistical learning has received increased attention in the past decade, due to spatially and temporally indexed data proliferation, especially collected from satellite remote sensing. In the mean time, observational studies of clouds are recognized as an important step to improve cloud representation in weather and climate models. Since 2006, the satellite CloudSat of NASA carries a 94 GHz cloud profiling radar and is able to retrieve, from radar reflectivity, microphysical parameter distribution such as water or ice content. The collected data is piled up with the successive satellite orbits of nearly two hours, leading to a large compressed database of 2 Tb (http://cloudsat.atmos.colostate.edu/). These observations give the opportunity to extend the cloud microphysical properties beyond the actual measurement locations using an interpolation and prediction algorithm. In order to do so, we introduce a statistical estimator based on the spatiotemporal covariance and mean of the observations known as kriging. An adequate parametric model for the covariance and the mean is chosen from an exploratory data analysis. Beforehand, it is necessary to estimate the parameters of this spatiotemporal model; This is performed in a Bayesian setting. The approach is then applied to a subset of the CloudSat dataset.

Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions.

Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

Study of a Modified Kumaraswamy Distribution

In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on (0,1), called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed.

Plasma-Profile Control in an ICP Reactor

ICP is widely used in electromagnetic scattering due to its high electron density and simple structure. The distribution of plasma parameters can affect the electromagnetic scattering, so the control of plasma parameter distribution is very important for aircraft stealth. Firstly, the effect of the number of coil turns on the plasma parameter distribution is analyzed. With the increase of the number of coil turns, the peak value of induced magnetic field decrease, the width of magnetic field increase and the homogeneity of plasma increase. Then, the Boltzmann solver is used to calculate the plasma electron energy distribution function at different positions under the four-turn coil. Finally, the influence of external circuit capacitance on plasma parameter distribution is analyzed. In this cavity structure, the electron density first increases and then decreases with the external circuit capacitance increase, and the peak value is on 75 pF. In this study, we propose a method to further regulate the plasma parameter distribution by using terminal capacitance to control the induced magnetic field.