Probability Distribution Random Variable (93 results)

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Statistical distance refers to either to measures of the distance of an observation from a population or to measures of the distances between populations. In the later case, the distances can be interpreted as measuring the distances berween two probability distributions and hence are essentially measures of distances between probability measures. In some contexts, statistical distance measures relate to the differences between random variables which may have statistical dependence, and hence these are not directly related to measures of distances between probability measures.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The coefficient of variation should only be computed for data measured on a ratio scale. As an example, if a group of temperatures are analyzed, the standard deviation does not depend on whether the Kelvin or Celsius scale is used. However the mean temperature of the data set would differ in each scale and thus the coefficient of variation would differ. So the coefficient of variation does not have any meaning for data on an interval scale.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory, a probability density function (abbreviated as pdf, or just density) of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point in the observation space. The probability of a random variable falling within a given set is given by the integral of its density over the set.On rare occasions the term probability distribution function is used to denote the probability density function. However special care should be taken around this term, since in other sources the probability distribution function may refer to either the probability distribution function, or the cumulative distribution function, or may be a probability mass function rather than a density.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! A phase-type distribution is a probability distribution that results from a system of one or more inter-related Poisson processes occurring in sequence, or phases. The sequence in which each of the phases occur may itself be a stochastic process. The distribution can be represented by a random variable describing the time until absorption of a Markov process with one absorbing state. Each of the states of the Markov process represents one of the phases.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector. In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable when the variable is discrete, or the probability of the value falling within a particular interval when the variable is continuous. The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any measurable subset of that range.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Regular conditional probability is a concept that has developed to overcome certain difficulties in formally defining conditional probabilities for continuous probability distributions. It is defined as an alternative probability measure conditioned on a particular value of a random variable. The difficulty with this arises when the event B is too small to have a non-zero probability. For example, suppose we have a random variable X with a uniform distribution on [0,1], and B is the event that X = 2 / 3. Clearly the probability of B in this case is P(B)=0, but nonetheless we would still like to assign meaning to a conditional probability such as P(A X=2/3). To do so rigorously requires the definition of a regular conditional probability.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory, the slash distribution is the probability distribution of a standard normal variate divided by an independent standard uniform variate. In other words, if the random variable Z has a normal distribution with zero mean and unit variance, the random variable U has a uniform distribution on [0,1] and Z and U are statistically independent, then the random variable X = Z / U has a slash distribution. The slash distribution is an example of a ratio distribution. The distribution was named by William H. Rogers and John Tukey in a paper published in 1972.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. A random vector is said to be multivariate normally distributed if every linear combination of its components has a univariate normal distribution.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The Skellam distribution is the discrete probability distribution of the difference n1 n2 of two statistically independent random variables n1 and n2 each having Poisson distributions with different expected values 1 and 2. It is useful in describing the statistics of the difference of two images with simple photon noise, as well as describing the point spread distribution in certain sports where all scored points are equal, such as baseball, hockey and soccer. The distribution is also applicable to a special case of the difference of dependent Poisson random variables, but just the obvious case where the two variables have a common additive random contribution which is cancelled by the differencing: see Karlis & Ntzoufras (2003) for details and an application.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! Variable-order Markov models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain models, where each random variable in a sequence with a Markov property depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on the specific observed realization. This realization sequence is often called the context; therefore the VOM models are also called context trees. The flexibility in the number of conditioning random variables turns out to be of real advantage for many applications, such as statistical analysis, classification and prediction.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the Gumbel distribution (named after Emil Julius Gumbel (1891 1966)) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. For example we would use it to represent the distribution of the maximum level of a river in a particular year if we had the list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The Tsallis distribution, also kown as a q-Gaussian, is a probability distribution arising from the optimisation of the Tsallis entropy. It is essentially a simple reparametrization of the Student's t-distribution introduced by W. Gosset in 1908 to describe small sample statistics. In Gosset's original presentation the degrees of freedom parameter was constrained to be a positive integer related to the sample size, but it is readily observed that Gosset's density function is valid for all real values of .

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the continuous uniform distribution is a family of probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U a,b. In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable, when the variable is discrete, or the probability of the value falling within a particular interval, when the variable is continuous.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In statistics, rankits of a set of data are the expected values of the order statistics of a sample from the standard normal distribution the same size as the data. They are primarily used in the normal probability plot, a graphical technique for normality testing. A graph plotting the rankits on the horizontal axis and the data points on the vertical axis is called a rankit plot (sometimes called normal probability plot). Such a plot is necessarily nondecreasing. In large samples from a normally distributed population, such a plot will approximate a straight line. Substantial deviations from straightness are considered evidence against normality of the distribution.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the discrete uniform distribution is a discrete probability distribution that can be characterized by saying that all values of a finite set of possible values are equally probable. In case the values of a random variable with a discrete uniform distribution are real, it is possible to express the cumulative distribution function in terms of the degenerate distribution.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the zeta distribution is a discrete probability distribution. If X is a zeta-distributed random variable with parameter s, then the probability that X takes the integer value k is given by the probability mass function f_s(k)=k^{-s}/zeta(s), where (s) is the Riemann zeta function (which is undefined for s = 1).The series on the right is just a series representation of the Riemann zeta function, but it only converges for values of s-n that are greater than unity.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The odds ratio is a measure of effect size, describing the strength of association or non-independence between two binary data values. It is used as a descriptive statistic, and plays an important role in logistic regression. Unlike other measures of association for paired binary data such as the relative risk, the odds ratio treats the two variables being compared symmetrically, and can be estimated using some types of non-random samples. The odds ratio is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that ratio. These groups might be men and women, an experimental group and a control group, or any other dichotomous classification. If the probabilities of the event in each of the groups are p1 (first group) and p2 (second group), then the odds ratio is: { p_1/(1-p_1) over p_2/(1-p_2)}={ p_1/q_1 over p_2/q_2}=frac{;p_1q_2;}{;p_2q_1;}, where qx = 1 px. An odds ratio of 1 indicates that the condition or event under study is equally likely to occur in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory, a probability density function of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point in the observation space. The probability of a random variable falling within a given set is given by the integral of its density over the set. On rare occasions the term probability distribution function is used to denote the probability density function. However special care should be taken around this term, since in other sources the probability distribution function may refer to either the probability distribution function, or the cumulative distribution function, or may be a probability mass function rather than a density.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the probit function is the inverse cumulative distribution function, or quantile function associated with the standard normal distribution. It has applications in exploratory statistical graphics and specialized regression modeling of binary response variables. The idea of probit was published in 1934 by Chester Ittner Bliss in an article in Science on how to treat data such as the percentage of a pest killed by a pesticide. Bliss proposed transforming the percentage killed into a 'probability unit' which was linearly related to the modern definition. He included a table to aid other researchers to convert their kill percentages to his probit, which they could then plot against the logarithm of the dose and thereby, it was hoped, obtain a more or less straight line. Such a so-called probit model is still important in toxicology, as well as other fields.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its application to statistical inference in particular, its application to James Stein estimation and empirical Bayes methods.Suppose X is a normally distributed random variable with expectation and variance 2. Further suppose g is a function for which the two expectations E( g(X) (X ) ) and E( g (X) ) both exist (the existence of the expectation of any random variable is equivalent to the finiteness of the expectation of its absolute value).

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory, the probability space, or probability triple, is a concept which serves as a rigorous mathematical ground for the conventional idea of randomness. It is a mathematical model of a real-world situation where we recognize that certain things occur at random . The model works as following: first, at the outset of the experiment we attempt to envision all possible outcomes which might possibly happen, the set of all such outcomes is called the sample space . Second, we recognize that the elementary outcomes could be too little of practical use, and that the more complicated events, consisting possibly of many different elementary outcomes, are of more interest.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In directional statistics, the von Mises Fisher distribution is a probability distribution on the p 1 dimensional sphere in R. If p = 2 the distribution reduces to the von Mises distribution on the circle. The probability density function of the von Mises-Fisher distribution for the random p-dimensional unit vector x. The parameters Mu, and K, are called the mean direction and concentration parameter, respectively. The greater the value of K, the higher the concentration of the distribution around the mean direction Mu. The distribution is unimodal for K 0, and is uniform on the sphere for K=0.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-square distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution. It is named in honor of John Wishart, who first formulated the distribution in 1928. It is any of a family of probability distributions for nonnegative-definite matrix-valued random variables ('random matrices'). These distributions are of great importance in the estimation of covariance matrices in multivariate statistics.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In statistics, normality tests are used to determine whether a data set is well-modeled by a normal distribution or not, or to compute how likely an underlying random variable is to be normally distributed. More precisely, they are a form of model selection, and can be interpreted several ways, depending on one's interpretations of probability: In descriptive statistics terms, one measures a goodness of fit of a normal model to the data if the fit is poor then the data is not well modeled in that respect by a normal distribution, without making a judgment on any underlying variable. In frequentist statistics statistical hypothesis testing, one tests the data against the null hypothesis that it is normally distributed.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, the variance of a random variable or distribution is the expected, or mean, value of the square of the deviation of that variable from its expected value or mean. Thus the variance is a measure of the amount of variation within the values of that variable, taking account of all possible values and their probabilities or weightings (not just the extremes which give the range). For example, a perfect dice, when thrown, has expected value (1+2+3+4+5+6)/6 = 3.5, expected absolute deviation 1.5 (the mean of the equally likely absolute deviations (3.5 1, 3.5 2, 3.5 3, 4 3.5, 5 3.5, 6 3.5), giving 2.5, 1.5, 0.5, 0.5, 1.5, 2.5, but expected square deviation or variance of 35/12 2.9 (the mean of the equally likely squared deviations 1/4, 9/4, and 25/4).

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! The Cauchy distribution is an example of a ratio distribution. The random variable associated with this distribution comes about as the ratio of two Gaussian (normal) distributed variables with zero mean. Thus the Cauchy distribution is also called the normal ratio distribution. A number of researchers have considered more general ratio distributions. Two distribution often used in test-statistics, the t-distribution and the F-distribution, are also ratio distributions: The t-distributed random variable is the ratio of a Gaussian random variable divided by an independent chi-distributed random variable (i.e., the square root of a chi-square distribution), while the F-distributed random variable is the ratio of two independent chi-square distributed random variables.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! Calculation of the sum of normally distributed random variables is the simplest instance of random variable arithmetic, which can be quite complex based on the distributions of the random variables involved and their relationships. This means that the sum of two independent normally distributed random variables is normal, with mean the sum of the two means, and the variance the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations).

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous). The probability distribution describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range. The Normal distribution, often called the 'bell curve'. When the random variable takes values in the set of real numbers, the probability distribution is completely described by the cumulative distribution function, whose value at each real x is the probability that the random variable is smaller than or equal to x.

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! A ratio distribution (or quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. The Cauchy distribution is an example of a ratio distribution. The random variable associated with this distribution comes about as the ratio of two Gaussian (normal) distributed variables with zero mean. Thus the Cauchy distribution is also called the normal ratio distribution. A number of researchers have considered more general ratio distributions. Two distribution often used in test-statistics, the t-distribution and the F-distribution, are also ratio distributions: The t-distributed random variable is the ratio of a Gaussian random variable divided by an independent chi-distributed random variable (i.e., the square root of a chi-square distribution), while the F-distributed random variable is the ratio of two independent chi-square distributed random variables. Often the ratio distributions are heavy-tailed, and it may be difficult to work with such distributions and develop an associated statistical test. A method based on the median has been suggested as a 'work-around'.

Taschenbuch. Condition: Neu. Coefficient of Variation | Coefficient of Variation, Probability Theory, Statistics, Normalization Statistics, Statistical Dispersion, Probability Distribution, Standard Deviation, Random Variable | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130336516 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.