Bernoulli Distribution: A random variable x has a Bernoulli distribution with parameter 0 < p < 1 if P(x) = ì ï àï î 1-p, x=0 p, x=1 0, x à{0, 1} where P(A) is the probability of outcome A. The parameter p is often called the...
View Full DescriptionBeta Distribution: Suppose x1, x2, ... , xn are n independent values of a random variable uniformly distributed within the interval [0,1]. If you sort the values in ascending order, then the k-th value will have a beta distribution with parameters a = k, b = n-k+1. The density of...
View Full DescriptionBinomial Distribution: Used to describe an experiment, event, or process for which the probability of success is the same for each trial and each trial has only two possible outcomes. If a coin is tossed n number of times, the probability of a certain number of heads being observed in...
View Full DescriptionBivariate Normal Distribution: Bivariate normal distribution describes the joint probability distribution of two variables, say X and Y, that both obey the normal distribution. The bivariate normal is completely specified by 5 parameters: mx, my are the mean values of variables X and Y, respectively; sx, sy are the standard...
View Full DescriptionCentral Limit Theorem: The central limit theorem states that the sampling distribution of the mean approaches Normality as the sample size increases, regardless of the probability distribution of the population from which the sample is drawn. If the population distribution is fairly Normally-distributed, this approach to Normality will happen at...
View Full DescriptionChebyshev´s Theorem: For any positive constant ´k´, the probability that a random variable will take on a value within k standard deviations of the mean is at least 1 - 1/k2 . Browse Other Glossary Entries
View Full DescriptionChi-Square Distribution: The square of a random variable having standard normal distribution is distributed as chi-square with 1 degree of freedom. The sum of squares of ´n´ independently distributed standard normal variables has a Chi-Square distribution with ´n´ degrees of freedom. The distribution is typically used to compare multiple-sample count...
View Full DescriptionConditional Probability: When probabilities are quoted without specification of the sample space, it could result in ambiguity when the sample space is not self-evident. To avoid this, the sample space can be explicitly made known. The probability of an event A given sample space S, denoted by P(A|S), is nothing...
View Full DescriptionContinuous Sample Space: If a sample space contains an infinite number of sample points constituting a continuum, then such a sample space is said to be a continuous sample space. Browse Other Glossary Entries
View Full DescriptionConvolution of Distribution Functions: If F1(·) and F1(·) are distribution functions, then the function F(·) F(x) = ó õ F1(x-y) dF2(y) is called the convolution of distribution functions F1 and F2. This is often denoted as F = F1 *F2. The convolution F1 *F2 provides the distribution function of...
View Full DescriptionErlang Distribution: The Erlang distribution with parameters (n, m) characterizes the distribution of time intervals until the emergence of n events in a Poisson process with parameter m . The Erlang distribution is a special case of the gamma distribution . Browse Other Glossary Entries
View Full DescriptionExponential Distribution: The exponential distribution is a one-sided distribution completely specified by one parameter r > 0; the density of this distribution is f(x) = ì àî re-rx, x ³ 0 0, x < 0 The mean of the exponential distribution is 1/r. The exponential distribution is a...
View Full DescriptionF Distribution: The F distribution is a family of distributions differentiated by two parameters: m1 (degrees of freedom, numerator) and m2 (degrees of freedom, denominator). If x1 and x2 are independent random variables with a chi-square distribution with m1 and m2 degrees of freedom respectively, then the random variable f...
View Full DescriptionGamma Distribution: A random variable x is said to have a gamma-distribution with parameters a > 0 and l > 0 if its probability density p(x) is p(x) = ì ï àï î la G(a) xa-1 e-lx, x > 0; 0, Browse Other Glossary Entries
View Full DescriptionGaussian Distribution: See Normal Distribution. Browse Other Glossary Entries
View Full DescriptionGeometric Distribution: A random variable x obeys the geometric distribution with parameter p (0<p<1) if P{x=k} = p(1-p)k, k=0,1,2, ... . If a random variable obeys the Bernoulli distribution with probability of success p, then x might be the number of trials before the first "success" occurs. If...
View Full DescriptionLaw of Large Numbers: According to the Law of Large Numbers, the probability that the proportion of successes in a sample will differ from the population proportion by less than c ( any positive constant) approaches 1 as the sample size tends to infinity. Browse Other Glossary Entries
View Full DescriptionLog-Normal Distribution: A random variable X has a log-normal distribution if ln(X) is normally distributed. Browse Other Glossary Entries
View Full DescriptionStatistical Glossary Markov Chain: A Markov chain is a series of random values x1, x2, ... in which the probabilities associated with a particular value xi depend only on the prior value xi-1. For this reason, a Markov chain is a special case of "memoryless" random processes. The index "i"...
View Full DescriptionStatistical Glossary Markov Property: Markov property means "absence of memory" of a random process - that is, independence of conditional probabilities P( U(t1 > t) | U(t) ) on values U(t2 < t). In simpler words, this property means that future behavior depends only on the current state, but not...
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