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Continuous uniform distribution. One of the simplest examples of a discrete univariate distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc.
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
The first one is to answer a research question with descriptive study and the second one is to get knowledge about how attribute varies with individual effect of a variable in regression analysis. There are some ways to describe patterns found in univariate data which include graphical methods, measures of central tendency and measures of ...
The product of independent random variables X and Y may belong to the same family of distribution as X and Y: Bernoulli distribution and log-normal distribution. Example: If X 1 and X 2 are independent log-normal random variables with parameters (μ 1, σ 2 1) and (μ 2, σ 2 2) respectively, then X 1 X 2 is a log-normal random variable with ...
Univariate analysis involves describing the distribution of a single variable, including its central tendency (including the mean, median, and mode) and dispersion (including the range and quartiles of the data-set, and measures of spread such as the variance and standard deviation).
The midpoint of the distribution, +, is both the mean and the median of the uniform distribution. Although both the sample mean and the sample median are unbiased estimators of the midpoint, neither is as efficient as the sample mid-range, i.e. the arithmetic mean of the sample maximum and the sample minimum, which is the UMVU estimator of the ...
A frequency distribution shows a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data notably to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc.
Statistical theorists study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions. Mathematicians and statisticians like Gauss , Laplace , and C. S. Peirce used decision theory with probability distributions and loss functions (or utility functions ).