Statistics How To

Statistics Definitions > Dispersion Contents: What is Dispersion? What dispersion is used for Measures of Dispersion Example Absolute and relative measures What is Dispersion? Dispersion (also called scatter, spread, or variability) is a way of describing how spread out a set of data is. It refers to the degree to which data points are spread out … Read more

Statistics Definitions > Serial Correlation / Autocorrelation What is Serial Correlation / Autocorrelation? Autocorrelation, also known as serial correlation, measures the correlation between observations of a variable with itself at different time points. It is often used to analyze time series data, and it can be used to determine whether or not the data is … Read more

Statistics Definitions > Fisher Information What is Fisher information? In statistics, Fisher information (or just information) measures information about a parameter in a distribution; the more “information” in X, the more accurate an estimator will be at estimating the parameter θ. Fisher information measures how much information a random variable provides about an unknown parameter … Read more

Probability Distributions > Power Series Distributions Contents: What are power series distributions? Explicit PMF (Normalization Constant) Special properties Variations and compounds of power series distributions Power series vs power law distributions What are power series distributions? Power series distributions are discrete probability distributions on a subset of natural numbers. The distributions are named because they … Read more

Probability Distributions > Reciprocal distribution What is a Reciprocal Distribution? There isn’t a universal definition for the “reciprocal distribution.” Definitions from the literature include: Any distribution of a reciprocal of a random variable [1]). A reciprocal continuous random variable [2]. A synonym for the logarithmic distribution [3]. That said, most probability density functions (pdfs) for … Read more

Probability Distributions > Discrete Probability Distribution Contents: What is a Discrete Probability Distribution? Discrete Probability Distribution Examples Common discrete distributions Properties What is a Discrete Probability Distribution? A discrete probability distribution is a set of probabilities associated with the outcomes of a random variable. A discrete probability distribution is made up of discrete variables. Discrete … Read more

> Probability Distributions > lognormal distribution What is a lognormal distribution? A lognormal distribution is one where the logarithm of the variable of interest is normally distributed. Consequently, the lognormal variable itself is strictly positive (i.e., >0) and often right-skewed. This distribution is useful for modeling many real-world phenomena (e.g., infection incubation periods, mineral deposit … Read more

Statistics Definitions > Asymptotic Normality and the Asymptotic Normal Distribution Asymptotic Normality Asymptotic normality is a property of an estimator: an estimator that is asymptotically normal will have an approximately normal distribution as the sample size gets infinitely large. Asymptotic refers to how the distribution of an estimator behaves as the sample size gets larger … Read more

Probability Distributions > Mixture Distribution What is a Mixture Distribution? A mixture distribution is a distribution with two or more combined probability distributions; A new distribution is created by drawing random variables from two or more parents. The parent distributions can be univariate distributions or multivariate distributions. The distributions can be made up of different … Read more

Probability Distributions > Irwin-Hall Distribution What is the Irwin-Hall Distribution? The Irwin-Hall distribution, also known as the Uniform Sum Distribution, is a powerful mathematical tool with many practical applications. Named after proofs provided by Irwin and Hall in 1927 [1, 2], it helps to determine sums of random variables within problems such as statistics or … Read more