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nbinstat

Negative binomial mean and variance

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    Syntax

    M = nbinstat(R,P)
    [M,V] = nbinstat(R,P)

    Description

    M = nbinstat(R,P) returns the mean for the negative binomial distribution with R successes and probability P of success in a single trial.

    [M,V] = nbinstat(R,P) also returns the variance for the distribution.

    example

    Examples

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    Open Live Script

    Generate vectors of values for the number of successes and probability of success in each trial.

    P = 0.1:0.2:0.9;
R = 1:5;

    For each pair of elements in P and R, calculate the mean and variance for the corresponding negative binomial distribution.

    [M,V] = nbinstat(R,P)
    M = 1×5

    9.0000    4.6667    3.0000    1.7143    0.5556


    V = 1×5

   90.0000   15.5556    6.0000    2.4490    0.6173

    Each pair of elements in the vectors M and V contains the mean and variance for the negative binomial distributions corresponding to the pairs of elements at the same positions in P and R.

    Input Arguments

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    Number of successes, specified as a positive scalar value or an array of positive scalar values. The elements of R can be noninteger values. If both R and P are arrays, they must be the same size. If either R or P is a scalar, then nbinstat expands the scalar argument into a constant array of the same size as the other argument.

    Example: [3 1 7]

    Data Types: single | double

    Probability of success in a single trial, specified as a positive scalar value or an array of positive scalar values. The elements of P must be between 0 and 1. If both P and R are arrays, they must be the same size. If either P or R is a scalar, then nbinstat expands the scalar argument into a constant array of the same size as the other argument.

    Example: [0.5 0.25 0.75]

    Data Types: single | double

    Output Arguments

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    Mean for the negative binomial distribution, returned as a numeric scalar or an array of numeric scalars. M is the same size as R and P. Each element in M is the mean of the negative binomial distribution specified by the corresponding elements in R and P. For more information, see Mean.

    Data Types: single | double

    Variance for the negative binomial distribution, returned as a numeric scalar or an array of numeric scalars. V is the same size as R and P. Each element in V is the variance of the negative binomial distribution specified by the corresponding elements in R and P. For more information, see Variance.

    Data Types: single | double

    More About

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    Mean

    The mean m of the negative binomial distribution with r successes and probability p of success in each trial is given by the formula

    m=r(1−p)p.

    Variance

    The variance v of the negative binomial distribution with r successes and probability p of success in each trial is given by the formula

    v=r(1−p)p2.

    Extended Capabilities

    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    GPU Arrays
    Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

    Version History

    Introduced before R2006a

    See Also

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