BinomialProcess
✖
BinomialProcess
Details
- BinomialProcess is a discrete-time and discrete-state process.
- BinomialProcess at time n is the number of events in the interval 0 to n.
- The number of events in the interval 0 to n follows BinomialDistribution[n,p].
- The times between events are independent and follow GeometricDistribution[p].
- BinomialProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
https://wolfram.com/xid/0g7kkot5kfm-247pzw
https://wolfram.com/xid/0g7kkot5kfm-m4g6ct
https://wolfram.com/xid/0g7kkot5kfm-knal8
https://wolfram.com/xid/0g7kkot5kfm-1oqmo2
https://wolfram.com/xid/0g7kkot5kfm-ffwb5p
https://wolfram.com/xid/0g7kkot5kfm-vszhoq
Scope (11)Survey of the scope of standard use cases
Basic Uses (5)
Simulate an ensemble of paths:
https://wolfram.com/xid/0g7kkot5kfm-ps93d
https://wolfram.com/xid/0g7kkot5kfm-cwtdxi
Compare paths for different values of process parameter:
https://wolfram.com/xid/0g7kkot5kfm-2vtftp
https://wolfram.com/xid/0g7kkot5kfm-iru9n5
https://wolfram.com/xid/0g7kkot5kfm-1hrt14
https://wolfram.com/xid/0g7kkot5kfm-45b7g2
Estimate the distribution parameter from sample data:
https://wolfram.com/xid/0g7kkot5kfm-epi747
https://wolfram.com/xid/0g7kkot5kfm-cr21l1
Absolute correlation function:
https://wolfram.com/xid/0g7kkot5kfm-jwtank
Process Slice Properties (6)
Univariate SliceDistribution:
https://wolfram.com/xid/0g7kkot5kfm-uwzo02
https://wolfram.com/xid/0g7kkot5kfm-60x0dy
Univariate probability density:
https://wolfram.com/xid/0g7kkot5kfm-b2ql07
Compare to the probability density of BinomialDistribution:
https://wolfram.com/xid/0g7kkot5kfm-r7hjni
https://wolfram.com/xid/0g7kkot5kfm-nu5aq
Multi-time slice distribution:
https://wolfram.com/xid/0g7kkot5kfm-3y1dz5
High-order probability density function:
https://wolfram.com/xid/0g7kkot5kfm-szzcub
Compute the expectation of an expression:
https://wolfram.com/xid/0g7kkot5kfm-drrgim
Calculate the probability of an event:
https://wolfram.com/xid/0g7kkot5kfm-ml0csm
https://wolfram.com/xid/0g7kkot5kfm-7kl7gd
https://wolfram.com/xid/0g7kkot5kfm-60a6x
https://wolfram.com/xid/0g7kkot5kfm-54n7c1
https://wolfram.com/xid/0g7kkot5kfm-yf46lb
Find for what values of the parameter BinomialProcess is symmetric:
https://wolfram.com/xid/0g7kkot5kfm-qm6isg
https://wolfram.com/xid/0g7kkot5kfm-4pe3ri
https://wolfram.com/xid/0g7kkot5kfm-caif64
https://wolfram.com/xid/0g7kkot5kfm-47lxqo
https://wolfram.com/xid/0g7kkot5kfm-nasem5
Find for what values of the parameter BinomialProcess is mesokurtic:
https://wolfram.com/xid/0g7kkot5kfm-dg3qxd
https://wolfram.com/xid/0g7kkot5kfm-yud84b
Moment has no closed form for symbolic order:
https://wolfram.com/xid/0g7kkot5kfm-gmlas0
https://wolfram.com/xid/0g7kkot5kfm-kupkj
https://wolfram.com/xid/0g7kkot5kfm-6jz3hy
CentralMoment has no closed form for symbolic order:
https://wolfram.com/xid/0g7kkot5kfm-6ne1e6
https://wolfram.com/xid/0g7kkot5kfm-j6j83y
FactorialMoment and its generating function:
https://wolfram.com/xid/0g7kkot5kfm-oesmc6
https://wolfram.com/xid/0g7kkot5kfm-qux587
Cumulant has no closed form for symbolic order:
https://wolfram.com/xid/0g7kkot5kfm-dmnjr2
https://wolfram.com/xid/0g7kkot5kfm-sddn3s
Applications (4)Sample problems that can be solved with this function
A quality assurance inspector randomly selects a series of 10 parts from a manufacturing process that is known to produce 20% bad parts. Find the probability that the inspector gets at most one bad part:
https://wolfram.com/xid/0g7kkot5kfm-m3hmfn
The probability of selecting at most one bad part:
https://wolfram.com/xid/0g7kkot5kfm-9swgk
It is known that, on average, 50% of the residents in a city like a certain TV program. Find the probability that at least 55% of residents will report that they like a program, in a survey of 804 people from the city:
https://wolfram.com/xid/0g7kkot5kfm-nguh5w
The probability that at least 55% of the residents in the sample will like the program:
https://wolfram.com/xid/0g7kkot5kfm-hwclk5
A packet consisting of a string of symbols is transmitted over a noisy channel. Each symbol has a probability 0.0001 of being transmitted in error. Find the largest for which the probability of incorrect transmission (at least one symbol in error) is less than 0.001:
https://wolfram.com/xid/0g7kkot5kfm-zmm1n
The probability of an error in the transmission:
https://wolfram.com/xid/0g7kkot5kfm-xrhud0
Plot probability of a transmission error together with error limit:
https://wolfram.com/xid/0g7kkot5kfm-fo1g5a
Find the largest for which the probability of incorrect transmission is less than :
https://wolfram.com/xid/0g7kkot5kfm-4xhjgz
Find the price of a European call option after the third period in a multi-period binomial model, given that the initial price of the underlying is $100, strike price is $102, interest rate is 1% per period, and the stock moves up by 7% or down by a factor of 1/1.07:
https://wolfram.com/xid/0g7kkot5kfm-px1hl9
https://wolfram.com/xid/0g7kkot5kfm-z49bf8
https://wolfram.com/xid/0g7kkot5kfm-9d73o7
Properties & Relations (5)Properties of the function, and connections to other functions
Binomial process is weakly stationary only for p equal to 0:
https://wolfram.com/xid/0g7kkot5kfm-tngt3z
A BinomialProcess is the sum of a BernoulliProcess with :
https://wolfram.com/xid/0g7kkot5kfm-pevfub
https://wolfram.com/xid/0g7kkot5kfm-bwfatc
https://wolfram.com/xid/0g7kkot5kfm-n9f3g1
https://wolfram.com/xid/0g7kkot5kfm-xhjutr
Compare to the binomial process:
https://wolfram.com/xid/0g7kkot5kfm-20pmaz
https://wolfram.com/xid/0g7kkot5kfm-zh69we
https://wolfram.com/xid/0g7kkot5kfm-1w2t5p
The time between events in a binomial process follows a PascalDistribution:
https://wolfram.com/xid/0g7kkot5kfm-fs7qgn
Calculate times between changes:
https://wolfram.com/xid/0g7kkot5kfm-8rlf71
https://wolfram.com/xid/0g7kkot5kfm-mamvw0
https://wolfram.com/xid/0g7kkot5kfm-u6egop
Compare the data histogram to the estimated probability density function:
https://wolfram.com/xid/0g7kkot5kfm-463u8c
https://wolfram.com/xid/0g7kkot5kfm-22nlbu
Transition probability between two states:
https://wolfram.com/xid/0g7kkot5kfm-7457m7
https://wolfram.com/xid/0g7kkot5kfm-j8lng2
BinomialProcess is a special case of CompoundRenewalProcess:
https://wolfram.com/xid/0g7kkot5kfm-r6gscd
https://wolfram.com/xid/0g7kkot5kfm-uyjs0
https://wolfram.com/xid/0g7kkot5kfm-bhb8mv
Create empirical covariance functions:
https://wolfram.com/xid/0g7kkot5kfm-t310wl
https://wolfram.com/xid/0g7kkot5kfm-qc9zb2
https://wolfram.com/xid/0g7kkot5kfm-k6mlnz
https://wolfram.com/xid/0g7kkot5kfm-6o6i9y
Compare the covariance functions:
https://wolfram.com/xid/0g7kkot5kfm-g027vd
Neat Examples (1)Surprising or curious use cases
Simulate 500 paths from a binomial process:
https://wolfram.com/xid/0g7kkot5kfm-q7hoj9
Take a slice at 50 and visualize its distribution:
https://wolfram.com/xid/0g7kkot5kfm-8s9gfo
https://wolfram.com/xid/0g7kkot5kfm-g5fe1v
Plot paths and histogram distribution of the slice distribution at 50:
https://wolfram.com/xid/0g7kkot5kfm-kwifgz
Wolfram Research (2012), BinomialProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/BinomialProcess.html.
Text
Wolfram Research (2012), BinomialProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/BinomialProcess.html.
Wolfram Research (2012), BinomialProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/BinomialProcess.html.
CMS
Wolfram Language. 2012. "BinomialProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BinomialProcess.html.
Wolfram Language. 2012. "BinomialProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BinomialProcess.html.
APA
Wolfram Language. (2012). BinomialProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BinomialProcess.html
Wolfram Language. (2012). BinomialProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BinomialProcess.html
BibTeX
@misc{reference.wolfram_2024_binomialprocess, author="Wolfram Research", title="{BinomialProcess}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/BinomialProcess.html}", note=[Accessed: 10-January-2025
]}
BibLaTeX
@online{reference.wolfram_2024_binomialprocess, organization={Wolfram Research}, title={BinomialProcess}, year={2012}, url={https://reference.wolfram.com/language/ref/BinomialProcess.html}, note=[Accessed: 10-January-2025
]}