Wikidata:Property proposal/probability distribution related properties

probability distribution related properties

This is a proposal of several probability distribution related properties

support of a function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: support of a function (P10731) (Talk and documentation)

Description	the subset of the domain containing those elements which are not mapped to zero
Represents	support (Q1136376)
Data type	Mathematical expression
Template parameter	support at en:Template:Probability distribution
Domain	functions
Example 1	normal distribution (Q133871) → $\mathbb {R}$
Example 2	exponential distribution (Q237193) → $x\in [0,\infty )$
Source	Many
Robot and gadget jobs	Probably no

probability mass function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: probability mass function (P10732) (Talk and documentation)

Description	a function that gives the probability that a discrete random variable is exactly equal to some value
Represents	probability mass function (Q869887)
Data type	Mathematical expression
Template parameter	pdf at en:Template:Probability distribution
Domain	probability distribution
Example 1	Poisson distribution (Q205692) → ${\frac {\lambda ^{k}e^{-\lambda }}{k!}}$
Example 2	Bernoulli distribution (Q391371) → $p^{k}(1-p)^{1-k}$
Source	Many
Robot and gadget jobs	Probably no

cumulative distribution function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: cumulative distribution function (P10736) (Talk and documentation)

Description	the probability that X will take a value less than or equal to x
Represents	distribution function (Q386228)
Data type	Mathematical expression
Template parameter	cdf at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → ${\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sigma {\sqrt {2}}}}\right)\right]$
Example 2	exponential distribution (Q237193) → $1-e^{-\lambda x}$
Source	Many
Robot and gadget jobs	Probably no

quantile function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: quantile function (P10737) (Talk and documentation)

Description	the value at which the probability of the random variable is less than or equal to the given probability
Represents	quantile function (Q3489473)
Data type	Mathematical expression
Template parameter	quantile at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2F-1)$
Example 2	exponential distribution (Q237193) → $-{\frac {\ln(1-p)}{\lambda }}$
Source	Many
Robot and gadget jobs	Probably no

mean of a probability distribution

Originally proposed at Wikidata:Property proposal/Natural science

   Done: mean of a probability distribution (P10738) (Talk and documentation)

Description	the long-run average value of repetitions of the experiment it represents
Represents	expectation (Q200125)
Data type	Mathematical expression
Template parameter	mean at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\mu$
Example 2	exponential distribution (Q237193) → ${\frac {1}{\lambda }}$
Source	Many
Robot and gadget jobs	Probably no

median of a probability distribution

Originally proposed at Wikidata:Property proposal/Natural science

   Done: median of a probability distribution (P10739) (Talk and documentation)

Description	the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half
Represents	median (Q226995)
Data type	Mathematical expression
Template parameter	median at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\mu$
Example 2	exponential distribution (Q237193) → ${\frac {\ln 2}{\lambda }}$
Source	Many
Robot and gadget jobs	Probably no

mode of a probability distribution

Originally proposed at Wikidata:Property proposal/Natural science

   Done: mode of a probability distribution (P10740) (Talk and documentation)

Description	the value that appears most often in a set of data
Represents	mode (Q188224)
Data type	Mathematical expression
Template parameter	mode at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\mu$
Example 2	exponential distribution (Q237193) → 0
Source	Many
Robot and gadget jobs	Probably no

variance of a probability distribution

Originally proposed at Wikidata:Property proposal/Natural science

   Done: variance of a probability distribution (P10743) (Talk and documentation)

Description	the expectation of the squared deviation of a random variable from its mean
Represents	variance (Q175199)
Data type	Mathematical expression
Template parameter	mode at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\sigma ^{2}$
Example 2	exponential distribution (Q237193) → ${\frac {1}{\lambda ^{2}}}$
Source	Many
Robot and gadget jobs	Probably no

skewness of a probability distribution

Originally proposed at Wikidata:Property proposal/Natural science

   Done: skewness (P10744) (Talk and documentation)

Description	a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean
Represents	coefficient of skewness (Q330828)
Data type	Mathematical expression
Template parameter	skewness at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → 0
Example 2	exponential distribution (Q237193) → 2
Source	Many
Robot and gadget jobs	Probably no

excess kurtosis

Originally proposed at Wikidata:Property proposal/Natural science

   Done: excess kurtosis (P10745) (Talk and documentation)

Description	a measure of the "tailedness" of the probability distribution of a real-valued random variable
Represents	kurtosis (Q287251)
Data type	Mathematical expression
Template parameter	kurtosis at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → 0
Example 2	exponential distribution (Q237193) → 6
Source	Many
Robot and gadget jobs	Probably no

information entropy

Originally proposed at Wikidata:Property proposal/Natural science

   Done: information entropy (P10746) (Talk and documentation)

Description	the expected value (average) of the information contained in each message
Represents	information entropy (Q204570)
Data type	Mathematical expression
Template parameter	entropy at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → ${\tfrac {1}{2}}\ln(2\sigma ^{2}\pi \,e\,)$
Example 2	exponential distribution (Q237193) → $1-\ln \lambda$
Source	Many
Robot and gadget jobs	Probably no

moment-generating function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: moment-generating function (P10747) (Talk and documentation)

Description	an alternative specification of its probability distribution
Represents	moment-generating function (Q535587)
Data type	Mathematical expression
Template parameter	mgf at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\exp\{\mu t+{\frac {1}{2}}\sigma ^{2}t^{2}\}$
Example 2	exponential distribution (Q237193) → ${\frac {\lambda }{\lambda -t}},{\text{ for }}t<\lambda$
Source	Many
Robot and gadget jobs	Probably no

characteristic function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: characteristic function (P10735) (Talk and documentation)

Description	the Fourier transform of the probability density function
Represents	characteristic function (Q822139)
Data type	Mathematical expression
Template parameter	chat at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → $\exp\{i\mu t-{\frac {1}{2}}\sigma ^{2}t^{2}\}$
Example 2	exponential distribution (Q237193) → ${\frac {\lambda }{\lambda -it}}$
Source	Many
Robot and gadget jobs	Probably no

Fisher information

Originally proposed at Wikidata:Property proposal/Natural science

   Done: Fisher information (P10734) (Talk and documentation)

Description	a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X
Represents	Fisher information (Q1420659)
Data type	Mathematical expression
Template parameter	fisher at en:Template:Probability distribution
Domain	probability distribution
Example 1	normal distribution (Q133871) → ${\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}$
Example 2	exponential distribution (Q237193) → ${\frac {1}{\lambda ^{2}}}$
Source	Many
Robot and gadget jobs	Probably no

probability generating function

Originally proposed at Wikidata:Property proposal/Natural science

   Done: probability generating function (P10733) (Talk and documentation)

Description	a power series representation (the generating function) of the probability mass function of the random variable
Represents	probability-generating function (Q372071)
Data type	Mathematical expression
Template parameter	pgf at en:Template:Probability distribution
Domain	probability distribution
Example 1	Poisson distribution (Q205692) → $\exp(\lambda (z-1))$
Example 2	Bernoulli distribution (Q391371) → $q+pz$
Source	Many
Robot and gadget jobs	Probably no

Motivation

These properties may provide some useful information about probability distributions. GZWDer (talk) 21:15, 17 February 2017 (UTC)

Discussion

• Currently many of those properties have quite general names and are therefore likely to be used outside of the stated domain. Please use more narrow names if you want to focus on this domain. ChristianKl (talk) 22:38, 17 February 2017 (UTC)
  • Changed.--GZWDer (talk) 05:27, 18 February 2017 (UTC)

• Okay the names now look reasonable to me.  Weak support.
  Opensofias
  Tobias1984
  Arthur Rubin
  Cuvwb
  TomT0m
  Physikerwelt
  Lymantria
  Bigbossfarin
  Infovarius
  Helder
  PhilMINT
  Malore
  Lore.mazza51
  Wikisaurus
  The Anome
  The-erinaceous-one
  Daniel Mietchen
  Haansn08
  Xenmorpha
  John Samuel
  Jeremy Dover
  Toni 001
  Bocardodarapti
  Duckmather
  HTinC23
  fgnievinski
  Paul-Olivier Dehaye
  uni
  Dexxor
  慈居
  Notified participants of WikiProject Mathematics ChristianKl (talk) 16:33, 18 February 2017 (UTC)

•  Support except for probability density function which is essentially what the "defining formula" should be for a probability distribution - note the previous discussion on this: Wikidata:Property proposal/probability density function. ArthurPSmith (talk) 16:58, 20 February 2017 (UTC)
• @GZWDer, ChristianKl: insufficient support for so many (16) new properties and no activity in over 3 months, so marked as  Not done. If you think this should be revived, this could be reopened, but I'd recommend picking just a few of these properties to focus on next time, with some more interesting examples to motivate this. ArthurPSmith (talk) 18:41, 14 June 2017 (UTC)
• @GZWDer, ChristianKl, ArthurPSmith: I would like to reopen these proposals, since they are indeed needed for around 170 distribution items, and really nobody opposed them (except for probability density function per this discussion). --Tinker Bell ★ ♥ 06:41, 25 April 2022 (UTC)
• Opensofias
  Tobias1984
  Arthur Rubin
  Cuvwb
  TomT0m
  Physikerwelt
  Lymantria
  Bigbossfarin
  Infovarius
  Helder
  PhilMINT
  Malore
  Lore.mazza51
  Wikisaurus
  The Anome
  The-erinaceous-one
  Daniel Mietchen
  Haansn08
  Xenmorpha
  John Samuel
  Jeremy Dover
  Toni 001
  Bocardodarapti
  Duckmather
  HTinC23
  fgnievinski
  Paul-Olivier Dehaye
  uni
  Dexxor
  慈居
  Notified participants of WikiProject Mathematics @Tinker Bell: Your support combined with GZWDer and me seems likely sufficient, but it's been a long time so pinging math participants again ArthurPSmith (talk) 15:09, 25 April 2022 (UTC)
•  Support Looks good to me! Bigbossfarin (talk) 15:42, 25 April 2022 (UTC)
•  Support These would be nice to have! One question though: what is the motivation for calling the expected value property "mean of a probability distribution" instead of simply "expected value?" I also think we should consider how we define the variables (parameters) used in in each mathematical expression. — The Erinaceous One 🦔
•  Support Same question as above: How to explain the variables? We could use a scheme similar to the one used for defining formula (P2534): Create a new property "parameters/symbols of probability distribution" and use the symbol represents (P9758) qualifier on that new property. Toni 001 (talk) 08:06, 26 April 2022 (UTC)
•  Support John Samuel (talk) 09:56, 26 April 2022 (UTC)
•  Comment Thanks everybody, I've marked these proposals all as ready. On parameter or variable naming, I would hope that consistent variable names are used across the different formulas for one distribution, so that they need only be defined once (and defining formula and our established rules there could work for that). ArthurPSmith (talk) 18:11, 26 April 2022 (UTC)

  Indeed. Given that the probability density function is given in the defining formula (P2534) the explanation of variables is solved. Toni 001 (talk) 08:02, 27 April 2022 (UTC)

@GZWDer, ChristianKl, ArthurPSmith, Tinker Bell, Tinker Bell: @The-erinaceous-one, Toni 001, Jsamwrites:  Done support of a function (P10731), probability mass function (P10732), cumulative distribution function (P10736), quantile function (P10737), mean of a probability distribution (P10738), median of a probability distribution (P10739), mode of a probability distribution (P10740), variance of a probability distribution (P10743), skewness (P10744), excess kurtosis (P10745), information entropy (P10746), moment-generating function (P10747), characteristic function (P10735), Fisher information (P10734), probability generating function (P10733) Pamputt (talk) 11:42, 10 May 2022 (UTC)