empirical probability การใช้

• In statistical terms, the empirical probability is an " estimate " or estimator of a probability.
• Statistical quantities computed from realizations without deploying a statistical model are often called " empirical ", as in empirical distribution function or empirical 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.
• 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.
• 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 De Moivre, Laplace, 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.
• The term " a-posteriori probability ", in its meaning as equivalent to "'empirical probability "', may be used in conjunction with " a priori probability " which represents an estimate of a probability not based on any observations, but based an deductive reasoning.
• Formally, a given two-sided context ( l ^ k, r ^ k ) \ in \ mathcal { Z } ^ k \ times \ mathcal { Z } ^ k that appears once or more along z ^ n determines an empirical probability distribution over \ mathcal { Z }, whose value at the symbol z is