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The only memoryless continuous probability distribution is the exponential distribution, shown in the following proof: [9] First, define S ( t ) = Pr ( X > t ) {\displaystyle S(t)=\Pr(X>t)} , also known as the distribution's survival function .
A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
If Alice knows the true distribution , while Bob believes (has a prior) that the distribution is , then Bob will be more surprised than Alice, on average, upon seeing the value of X. The KL divergence is the (objective) expected value of Bob's (subjective) surprisal minus Alice's surprisal, measured in bits if the log is in base 2.
(This formula is sometimes called the Hartley function.) This is the maximum possible rate of information that can be transmitted with that alphabet. (The logarithm should be taken to a base appropriate for the unit of measurement in use.) The absolute rate is equal to the actual rate if the source is memoryless and has a uniform distribution.
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 capacity of a discrete memoryless channel can be computed using the Blahut-Arimoto algorithm. Deep learning can be used to estimate the channel capacity. In fact, the channel capacity and the capacity-achieving distribution of any discrete-time continuous memoryless vector channel can be obtained using CORTICAL, [ 9 ] a cooperative ...
The distribution of a random variable that is defined as the minimum of several random variables, each having a different Weibull distribution, is a poly-Weibull distribution. The Weibull distribution was first applied by Rosin & Rammler (1933) to describe particle size distributions.