WOLFRAM

represents a binomial process with event probability p.

Details

Examples

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Basic Examples  (3)Summary of the most common use cases

Simulate a binomial process:

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Mean and variance functions:

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Covariance function:

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Scope  (11)Survey of the scope of standard use cases

Basic Uses  (5)

Simulate an ensemble of paths:

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Compare paths for different values of process parameter:

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Process parameter estimation:

Estimate the distribution parameter from sample data:

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Correlation function:

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Absolute correlation function:

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Process Slice Properties  (6)

Univariate SliceDistribution:

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Univariate probability density:

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Compare to the probability density of BinomialDistribution:

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Multi-time slice distribution:

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High-order probability density function:

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Compute the expectation of an expression:

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Calculate the probability of an event:

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Skewness:

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The limiting values:

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Find for what values of the parameter BinomialProcess is symmetric:

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Kurtosis:

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The limiting values:

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Find for what values of the parameter BinomialProcess is mesokurtic:

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Moment has no closed form for symbolic order:

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Generating functions:

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CentralMoment has no closed form for symbolic order:

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FactorialMoment and its generating function:

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Cumulant has no closed form for symbolic order:

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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:

The probability of selecting at most one bad part:

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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:

The probability that at least 55% of the residents in the sample will like the program:

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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:

The probability of an error in the transmission:

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Plot probability of a transmission error together with error limit:

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Find the largest for which the probability of incorrect transmission is less than :

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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:

Model the process:

Price of the call option:

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Properties & Relations  (5)Properties of the function, and connections to other functions

Binomial process is weakly stationary only for p equal to 0:

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A BinomialProcess is the sum of a BernoulliProcess with :

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Accumulate the sample:

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Compare to the binomial process:

Align time stamps:

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The time between events in a binomial process follows a PascalDistribution:

Calculate times between changes:

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Fit a Pascal distribution:

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Compare the data histogram to the estimated probability density function:

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Check goodness of fit:

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Transition probability between two states:

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BinomialProcess is a special case of CompoundRenewalProcess:

The mean functions agree:

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Create empirical covariance functions:

Compare the covariance functions:

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Neat Examples  (1)Surprising or curious use cases

Simulate 500 paths from a binomial process:

Take a slice at 50 and visualize its distribution:

Plot paths and histogram distribution of the slice distribution at 50:

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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.

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 ]}

@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 ]}

@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 ]}