Mathematical Statistics for Beginners
A significant number of discrete and continuous probability distributions are already accessible. A probability distribution’s mean, variance, skewness, and kurtosis are a collection of constants that can be used to describe its attributes and, in certain cases, to specify it. These constants are determined by the random variable’s distribution. To find the mean, variance, skewness, and kurtosis of any probability distribution, extensive understanding of integration, differentiation, and summation is necessary. It’s difficult to explain things to students who don’t know much about math. Instead than using integration, differentiation, or summation procedures, this book developed and utilised universal equations to directly find mean, variance, skewness, and kurtosis. We derive and apply universal formulae for determining the characteristic function, Laplace transform, and moments of various distributions from the converted Chi-square family, generalised gamma family, generalised family of discrete distributions, and log type distributions. This book also includes generic equations for determining point and interval estimators of function of parameters, as well as identification of the best population in the converted Chi-square family, as well as the likelihood of correct identification. This book teaches you how to choose null and alternative hypotheses, calculate p-values, and make conclusions using a simple procedure.
M. Shafiqur Rahman
Department of Operations Management and Business Statistics College of Economics and Political Science Sultan Qaboos University Muscat, Sultanate of Oman.
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characteristic function generalized gamma family kurtosis Laplace transform and moments log-type distributions mean. Probability distributions skewness tests of hypotheses transformed chi-square family variance