Concepts inAlgorithm 780: exponential pseudorandom distribution
Randomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability (or lack thereof) of events. The Oxford English Dictionary defines 'random' as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc. , without method or conscious choice; haphazard.
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Pseudorandomness
A pseudorandom process is a process that appears to be random but is not. Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process. Such a process is easier to produce than a genuinely random one, and has the benefit that it can be used again and again to produce exactly the same numbers - useful for testing and fixing software.
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Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values. For a more precise definition one needs to distinguish between discrete and continuous random variables. In the discrete case, one can easily assign a probability to each possible value: when throwing a die, each of the six values 1 to 6 has the probability 1/6.
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Exponential distribution
Exponential Parameters λ > 0 rate, or inverse scale Support x ∈ [0, ∞] PDF λ e CDF 1 − e Mean λ Median λ ln 2 Mode 0 Variance λ Skewness 2 Ex. kurtosis 6 Entropy 1 − ln(λ) In probability theory and statistics, the exponential distribution (a.k.a. negative exponential distribution) is a family of continuous probability distributions. It describes the time between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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Calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful relationship between two people. For example, multiplying 7 by 8 is a simple algorithmic calculation.
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Mathematics
"Maths" and "Math" redirect here. For other uses see Mathematics (disambiguation) and Math (disambiguation). Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of quantity, structure, space, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
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