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# Mathematical Statistics

DOI link for Mathematical Statistics

Mathematical Statistics book

# Mathematical Statistics

DOI link for Mathematical Statistics

Mathematical Statistics book

## ABSTRACT

The term “statistics” derives from the Latin word “status,” meaning “state.” Statistics comprises three major divisions: collection of statistical data, their statistical analysis, and development of mathematical methods for processing and using the statistical data to draw scientific and practical conclusions. It is the last division that is commonly known as mathematical statistics. The original material for a statistical study is a set of results specially gathered for this study or a set of results of specially performed experiments. The following problems arise in this connection. 1. Estimating the unknown probability of a random event 2. Finding the unknown theoretical distribution function

The problem is stated as follows. Given the values x1, . . . , xn of a random variable X obtained in n independent trials, find, at least approximately, the unknown distribution function F (x) of the random variable X. 3. Determining the unknown parameters of the theoretical distribution function

The problem is stated as follows. A random variable X has the distribution function F (x; θ1, . . . , θk) depending on k parameters θ1, . . . , θk, whose values are unknown. The main goal is to estimate the unknown parameters θ1, . . . , θk using only the results X1, . . . , Xn of observations of the random variable X.