geostat

Geometric mean and variance

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    Syntax

    [m,v] = geostat(p)

    Description

    [m,v] = geostat(p) returns the mean m and variance v of a geometric distribution with the corresponding probability parameter in p. For more information, see Geometric Distribution Mean and Variance.

    example

    Examples

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    Open Live Script

    Roll a fair die repeatedly until you successfully get a 6. The associated geometric distribution models the number of times you roll the die before the result is a 6. Determine the mean and variance of the distribution, and visualize the results.

    Because the die is fair, the probability of successfully rolling a 6 in any given trial is p = 1/6. Compute the mean and variance of the geometric distribution.

    p = 1/6;
[m,v] = geostat(p)
    m = 
5.0000

    v = 
30.0000

    Notice that the mean m is (1-p)/p and the variance v is (1-p)/p2.

    m2 = (1-p)/p
    m2 = 
5.0000

    v2 = (1-p)/p^2
    v2 = 
30.0000

    Evaluate the probability density function (pdf), or probability mass function (pmf), at the points x = 0,1,2,...,25.

    rng("default") % For reproducibility
x = 0:25;
y = geopdf(x,p);

    Plot the pdf values. Indicate the mean, one standard deviation below the mean, and one standard deviation above the mean. 

    bar(x,y,"FaceAlpha",0.2,"EdgeAlpha",0.2);
xline([m-sqrt(v) m m+sqrt(v)],"-", ...
    ["-1 Standard Dev.","Mean","+1 Standard Dev."])
xlabel(["Number of Rolls","Before Rolling a 6"])
ylabel("Probability")

    Figure contains an axes object. The axes object with xlabel Number of Rolls Before Rolling a 6, ylabel Probability contains 4 objects of type bar, constantline.

    Open Live Script

    Create a probability vector that contains three different parameter values.

    • The first parameter corresponds to a geometric distribution that models the number of times you toss a coin before the result is heads.

    • The second parameter corresponds to a geometric distribution that models the number of times you roll a four-sided die before the result is a 4.

    • The third parameter corresponds to a geometric distribution that models the number of times you roll a six-sided die before the result is a 6.

    p = [1/2 1/4 1/6];

    Compute the mean and variance of each geometric distribution.

    [m,v] = geostat(p)
    m = 1×3

    1.0000    3.0000    5.0000


    v = 1×3

    2.0000   12.0000   30.0000

    The returned values indicate that, for example, the mean of a geometric distribution with probability parameter p = 1/4 is 3, and the variance of the distribution is 12.

    Input Arguments

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    Probability of success in a single trial, specified as a scalar or an array of scalars in the range [0,1]. To compute the means and variances of multiple distributions, specify the distribution parameters p using an array of scalar values.

    Example: 0.5

    Example: [1/2 1/3]

    Data Types: single | double

    Output Arguments

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    Mean of the geometric distribution, returned as a numeric scalar or an array of numeric scalars. m is the same size as p, and each element in m is the mean of the geometric distribution specified by the corresponding element in p.

    Variance of the geometric distribution, returned as a numeric scalar or an array of numeric scalars. v is the same size as p, and each element in v is the variance of the geometric distribution specified by the corresponding element in p.

    More About

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    References

    [1] Abramowitz, M., and I. A. Stegun. Handbook of Mathematical Functions. New York: Dover, 1964.

    [2] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed., Hoboken, NJ: John Wiley & Sons, Inc., 1993.

    Extended Capabilities

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

    Version History

    Introduced before R2006a

    See Also

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    Topics