Model Assisted Statistics and Applications

First we study estimation of the drift parameter in the fractional Ornstein-Uhlenbeck process whose marginal distribution is Student t -distribution. We obtain Spearman’s correlation based estimator, quantile estimator and Brownian excursion based estimator of the drift parameter. Then we study method of moments estimator and quantile estimator in fractional inverse Gaussian and fractional gamma Ornstein-Uhlenbeck processes.

Network data arises naturally in a wide variety of applications in different fields. In this article we discuss in detail the statistical modeling of financial networks. The structure of such networks red has not been studied thoroughly in the past, mainly due to limited accessible data. We explore the structure of a real trading network corresponding to transactions within the natural gas future market over a four-year period. The detection of meaningful communities of actors within networks is particularly relevant to understand the topology of a complex system like this. We explore the usage of stochastic block models in conjunction with a nonparametric Bayesian approach in order to identify clusters of traders in a flexible modeling framework. Our findings strongly indicate that the proposed models are highly reliable at detecting community structures.

General classes of bivariate distributions are well-studied in the literature. Most of these classes are proposed via a copula formulation or extensions of some characterization properties in the univariate case. In Kundu (2022), we see one such semi-parametric family useful to model bivariate data with ties. This model is a general semi-parametric model with a baseline. In this paper, we present a characterization property of this class of distributions in terms of a functional equation. The general solution to this equation is explored. Necessary and sufficient conditions under which the solution becomes a bivariate distribution are investigated. An application of the characterization property of the proposed class for generating bivariate pairs of random variables from a member distribution is also discussed.

This paper investigates the moments of a stochastic process that satisfies the one-dimensional linear stochastic differential equation (SDE) with nonlinear time-dependent drift and diffusion coefficients. The goal is to derive formulas for the n th exact moment, that instead of seeking the transition density function by solving the Fokker-Plank equations or moment-generating functions, which can be difficult to solve in closed form. We will appropriately apply Itô’s formula and the properties of the Wiener process with a constant drift and diffusion term, which is a Gaussian process to obtain the exact higher-order moments.

Laplace probability density function with additional shape parameter that regulates the degree of skewness is a skew Laplace distribution. The various forms of skew Laplace distribution are found in the literature, the distributions defined by Mc Gill (1962), Holla and Bhattacharya (1968), Lingappaiah (1988), Fernandez and Steel (1998). The skew log Laplace distribution is the probability distribution of a random variable whose logarithm follows a skew Laplace distribution. In this paper, the classical optimum tests for skewness parameter of skew log Laplace distribution (SLLD) derived from Lingappaiah (1988) distribution are discussed. Uniformly most powerful test, uniformly most powerful unbiased test and Wald’s sequential probability ratio test for skewness parameter are compared. The exact likelihood ratio test and Neyman structure test for testing skewness parameter when scale parameter is known are derived. Finally, the underreported income of Road Transport Company is analysed on the basis of the tests derived in this paper.

In this study we develop a change point methodology to identify and estimate changes in the parameter of a Poisson distribution. The proposed methodology considers the case when the Poisson parameter changes abruptly at an unknown point of time. For this case, the maximum likelihood estimate of the change point and its asymptotic distribution are pursued. Mainly, we carry out a large scale simulation study for evaluating the appropriateness of the asymptotic distribution of the mle from the view point of finite samples, and also for evaluating the closeness under known and unknown parameters. The simulations study also compares the mle with that of a Bayesian estimate. Then, the methodology is applied to three examples. First, we uncover changes in the number of homicides in California using monthly data from January 2002 until December 2020. Secondly, data about deaths of females caused by stomach cancer is considered to detect possible changes in the numbers recorded from 1930 to 2011. Thirdly, British coal mining disasters from 1851 to 1962 in which more than 10 men were killed are analyzed.

Solid waste management has become a challenge for developing countries mainly because of surging economic activities, rapid urbanisation and rise in community living standards. Many researchers have identified its related problems and have recommended solutions while others have established models to forecast the amount of solid waste generated over a period. However, an efficient and effective management of solid waste requires adequate categorisation of solid waste generation areas to aid in the provision of area-specific or targeted solutions for each categorised area. In this study, we used primary data on some important socio-demographic variables (household size, house type, predominant religion of household, age and educational level of household head, residency type household waste disposal method, frequency of waste collection etc) and the amount of solid waste generated from 2102 households in Greater Accra Region, Ghana. We assessed the classification performances of a traditional statistical classifiers and some selected machine learning algorithms in classifying the surveyed areas in Greater Accra into low, medium, and high solid waste generation areas. The Support Vector Machine with the Cubic Kernel was found to be the best performing classifier with a Specificity of 86%, Sensitivity, Precision and Accuracy of 73% and Area under the curve (AUC) of 0.90. The Support Vector Machine with the Cubic Kernel is therefore recommended as a suitable algorithm for the categorisation of solid waste generation areas. Stakeholders responsible for solid waste management could leverage on the evidence from this study to categorise their waste generation areas and to proffer targeted community-based interventions.

In survey sampling, it is observed that researchers and users of statistics sometimes do not take into consideration the tool that will be most appropriate for the measure of location. As a result, they often go for the mean or total, which has wider coverage in the finite population sampling literature, unlike the median, which is more complicated to deal with given that it has to do with ordered data. Keeping in mind the established facts from the literature on the usefulness of the median estimator in estimating economic indicators for high precision and efficiency, this study has made useful improvement in estimating the population median not only for gains in efficiency but also in achieving less biased estimates. The study suggests an estimator of population median in single and double sampling techniques. In addition, minimum mean square error has also been obtained for a given cost function under double sampling. Results obtained from both theoretical and empirical investigations reveal that the proposed estimators perform better when the considered variables are from a highly skewed distribution, such as income, expenditure, scores, etc. Moreso, it is observed that the proposed estimators compete favorably with less bias and outstanding gains in efficiency than the existing estimators of its class. In addition, this study avails us of an appropriate way of constructing the cost function for better evaluations compared to an existing estimator considered in this work.