|
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution can be specified by a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution can be specified by a probability density function. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures. In applied probability, a probability distribution can be specified in a number of different ways, often chosen for mathematical convenience: *by supplying a valid probability mass function or probability density function *by supplying a valid cumulative distribution function or survival function *by supplying a valid hazard function *by supplying a valid characteristic function *by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known. A probability distribution can either be univariate or multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector—a set of two or more random variables—taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution. ==Introduction== To define probability distributions for the simplest cases, one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value: for example, when throwing a fair , each of the six values ''1'' to ''6'' has the probability 1/6. In contrast, when a random variable takes values from a continuum then, typically, probabilities can be nonzero only if they refer to intervals: in quality control one might demand that the probability of a "500 g" package containing between 490 g and 510 g should be no less than 98%. If the random variable is real-valued (or more generally, if a total order is defined for its possible values), the cumulative distribution function (CDF) gives the probability that the random variable is no larger than a given value; in the real-valued case, the CDF is the integral of the probability density function (pdf) provided that this function exists. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「probability distribution」の詳細全文を読む スポンサード リンク
|