empirical probability

In a more general sense, empirical probability estimates probabilities from experience and observation.

In statistical terms, the empirical probability is an estimate or estimator of a probability.

A direct estimate could be found by counting the number of men who satisfy both conditions to give the empirical probability of the combined condition.

The phrase a-posteriori probability is also used as an alternative to empirical probability or relative frequency.

An advantage of estimating probabilities using empirical probabilities is that this procedure is relatively free of assumptions.

The relative frequency (or empirical probability) of an event refers to the absolute frequency normalized by the total number of events:

A disadvantage in using empirical probabilities arises in estimating probabilities which are either very close to zero, or very close to one.

It follows from the law of large numbers that the empirical probability of success in a series of Bernoulli trials will converge to the theoretical probability.

Statistical quantities computed from realizations without deploying a statistical model are often called "empirical", as in empirical distribution function or empirical probability.

Here statistical models can help, depending on the context, and in general one can hope that such models would provide improvements in accuracy compared to empirical probabilities, provided that the assumptions involved actually do hold.

The term a-posteriori probability, in its meaning as equivalent to empirical probability, may be used in conjunction with a priori probability which represents a estimate of a probability not based on any observations, but based an deductive reasoning.

Under this "standard" NPV approach, future expected cash flows are present valued under the empirical probability measure at a discount rate that reflects the embedded risk in the project; see CAPM, APT, WACC.

The empirical probability, also known as relative frequency, or experimental probability, is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

The refinement of Bernoulli's Golden Theorem, regarding the convergence of theoretical probability and empirical probability, was taken up by many notable later day mathematicians like Poisson, Chebyshev, Markov, Borel, Cantelli, Kolmogorov and Khinchin.

If a trial yields more information, the empirical probability can be improved on by adopting further assumptions in the form of a statistical model: if such a model is fitted, it can be used to derive an estimate of the probability of the specified event.

In economics, the Lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth; it is a graph showing the proportion of the distribution assumed by the bottom y% of the values (although this is not rigorously true for a finite population - see below).