Probability and Statistics

Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology.

put the theory of mathematical probability on a sound footing

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution o

In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distrib

In probability theory, de Finetti's theorem states that exchangeable observations are conditionally independent relative to some l

In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) f

In mathematics and statistics, Skorokhod's representation theorem is a result that shows that a weakly convergent sequence of prob

In probability theory, Kolmogorov's three-series theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure con

In probability theory, Kolmogorov's inequality is a so-called "maximal inequality" that gives a bound on the probability that the

In probability theory, Azuma's inequality or the Azuma-Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) give

In mathematics and probability theory, Skorokhod's embedding theorem is either or both of two theorems that allow one to regard an

In probability theory, the law of large numbers is a mathematical law which states that the average of the results obtained from a

In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests.

In statistics, the delta method is a method of deriving the asymptotic distribution of a random variable.

In statistics, Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and sample standard dev

In statistics, the Fisher transformation (or Fisher z-transformation) of a Pearson correlation coefficient is its inverse hyperbol

In mathematics and statistics, the arithmetic mean ( arr-ith-MET-ik), arithmetic average, or just the mean or average is the sum o

In statistics, the probit function converts a probability (a number between 0 and 1) into a score.

In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes

In probability theory and statistics, covariance is a measure of the joint variability of two random variables.

In probability theory and statistics, the zeta distribution is a discrete probability distribution.

In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of

In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMS

In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data.

In statistics, the Bhattacharyya distance is a quantity which represents a notion of similarity between two probability distributi

In statistics, the percentile rank (PR) of a given score is the percentage of scores in its frequency distribution that are less t

In statistics, Spearman's rank correlation coefficient or Spearman's ρ is a number ranging from −1 to 1 that indicates how strongl

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete

In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals

In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (

In statistics, the logit (logistic unit) or log-odds function is the quantile function associated with the standard logistic distr

In statistics and in probability theory, distance correlation is a measure of dependence between two paired random vectors of arbi

In statistics, a zero-inflated model is a statistical model based on a zero-inflated probability distribution, i.e.

In probability theory and statistics, a standardized moment of a probability distribution is a moment (often a higher degree centr

In probability theory, an empirical process is a stochastic process that characterizes the deviation of the empirical distribution

In descriptive statistics, the range of a set of data is the size or width of the narrowest interval which contains all the data.

In statistics, the Pearson correlation coefficient (PCC), also known as Pearson's r, the Pearson product-moment correlation coeffi

In probability theory and directional statistics, the von Mises distribution (also known as the circular normal distribution or th

In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or sque

In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the sq

In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible e

In probability theory and statistics, the Poisson distribution () is a discrete probability distribution that expresses the probab

In probability theory and statistics, the Weibull distribution is a continuous probability distribution.

In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent rando

In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under ch

In probability theory, the central limit theorem states that, under certain circumstances, the probability distribution of the sca

In probability theory, Wald's equation, Wald's identity or Wald's lemma is an important identity that simplifies the calculation o

In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its m

In probability theory, Le Cam's theorem, named after Lucien Le Cam, states the following.

In statistics, Basu's theorem states that any boundedly complete and sufficient statistic is independent of any ancillary statisti

In statistics, Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produc

In probability theory, Cantelli's inequality (also called the Chebyshev-Cantelli inequality and the one-sided Chebyshev inequality

In probability theory, the continuous mapping theorem states that continuous functions preserve limits even if their arguments are

In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian mo

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