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Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. (Buffon's needle) What is the chance that a needle dropped randomly onto a floor marked with equally spaced parallel lines will cross one of the lines?
The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution . [ 1 ] : 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.
The Gauss–Kuzmin distribution; The geometric distribution, a discrete distribution which describes the number of attempts needed to get the first success in a series of independent Bernoulli trials, or alternatively only the number of losses before the first success (i.e. one less). The Hermite distribution; The logarithmic (series) distribution
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
This is the case that maximizes the geometric mean of such spacings, so solving for the parameters that maximize the geometric mean would achieve the “best” fit as defined this way. Ranneby (1984) justified the method by demonstrating that it is an estimator of the Kullback–Leibler divergence , similar to maximum likelihood estimation ...
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.
Furthermore, it was shown by Fackler [2] that there is a universal formula for all three distributions, called the (united) Panjer distribution. The more usual parameters of these distributions are determined by both a and b. The properties of these distributions in relation to the present class of distributions are summarised in the following ...
Moduli spaces are spaces of solutions of geometric classification problems. That is, the points of a moduli space correspond to solutions of geometric problems. Here different solutions are identified if they are isomorphic (that is, geometrically the same). Moduli spaces can be thought of as giving a universal space of parameters for the problem.
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