Probability and statistics

probability, statistics
Probability and statistics, also called statistics and probability, are two related but separate academic disciplines.wikipedia
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Statistics

statisticalstatistical analysisstatistician
Statistical analysis often uses probability distributions, and the two topics are often studied together.
The earliest writings on probability and statistics, statistical methods drawing from probability theory, date back to Arab mathematicians and cryptographers, notably Al-Khalil (717–786) and Al-Kindi (801–873).

Probability theory

theory of probabilityprobabilityprobability theorist
However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics.
The earliest known forms of probability and statistics were developed by Arab mathematicians studying cryptography between the 8th and 13th centuries.

Discipline (academia)

academic disciplinedisciplinesdiscipline
Probability and statistics, also called statistics and probability, are two related but separate academic disciplines.

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
Statistical analysis often uses probability distributions, and the two topics are often studied together.

Mathematics

mathematicalmathmathematician
However, probability theory contains much that is mostly of mathematical interest and not directly relevant to statistics.

Mathematics in medieval Islam

mathematicianmathematicsIslamic mathematics
Forms of probability and statistics were developed by Arab mathematicians studying cryptology between the 8th and 13th centuries.

Cryptography

cryptographiccryptographercryptology
Forms of probability and statistics were developed by Arab mathematicians studying cryptology between the 8th and 13th centuries.

Al-Khalil ibn Ahmad al-Farahidi

Al-KhalilKhalil ibn AhmadAl-Farahidi
Al-Khalil (717–786) wrote the Book of Cryptographic Messages which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.

Twelvefold way

permutations and combinationscombinationcombinations
Al-Khalil (717–786) wrote the Book of Cryptographic Messages which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.

Arabic

Arabic languageArabic-languageArab
Al-Khalil (717–786) wrote the Book of Cryptographic Messages which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.

Al-Kindi

AlkindusAl-KindīAl Kindi
Al-Kindi (801–873) made the earliest known use of statistical inference in his work on cryptanalysis and frequency analysis.

Statistical inference

inferential statisticsinferenceinferences
Al-Kindi (801–873) made the earliest known use of statistical inference in his work on cryptanalysis and frequency analysis.

Cryptanalysis

cryptanalystcodebreakingcodebreaker
Al-Kindi (801–873) made the earliest known use of statistical inference in his work on cryptanalysis and frequency analysis.

Frequency analysis

Frequency analysis (cryptanalysis)frequenciesfrequency analyzed
Al-Kindi (801–873) made the earliest known use of statistical inference in his work on cryptanalysis and frequency analysis.

Ibn 'Adlan

Ibn Adlan
An important contribution of Ibn Adlan (1187–1268) was on sample size for use of frequency analysis.

Sample size determination

sample sizeSampling sizessample
An important contribution of Ibn Adlan (1187–1268) was on sample size for use of frequency analysis.

Random variable

random variablesrandom variationrandom
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is described informally as a variable whose values depend on outcomes of a random phenomenon.

Compound probability distribution

compound distributionmixturecompounding
In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.

Generalized beta distribution

generalized beta distribution of the first kindgeneralized beta distribution of the second kindgeneralized Beta II (GB2)
In probability and statistics, the generalized beta distribution is a continuous probability distribution with five parameters, including more than thirty named distributions as limiting or special cases.

Gompertz distribution

Gompertz
In probability and statistics, the Gompertz distribution is a continuous probability distribution, named after Benjamin Gompertz.

Inverse-chi-squared distribution

inverse of the chi-squared functionInverse-chi-square distribution
In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution ) is a continuous probability distribution of a positive-valued random variable.