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betastat


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 -- statistics: [M, V] = betastat (A, B)

     Compute statistics of the Beta distribution.

     Arguments
     ---------

        • A is the first parameter of the beta distribution.  A must be
          positive

        • B is the second parameter of the beta distribution.  B must be
          positive
     A and B must be of common size or one of them must be scalar

     Return values
     -------------

        • M is the mean of the beta distribution

        • V is the variance of the beta distribution

     Examples
     --------

          a = 1:6;
          b = 1:0.2:2;
          [m, v] = betastat (a, b)

          [m, v] = betastat (a, 1.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the Beta distribution.



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binostat


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 -- statistics: [M, V] = binostat (N, P)

     Compute statistics of the binomial distribution.

     Arguments
     ---------

        • N is the first parameter of the binomial distribution.  The
          elements of N must be natural numbers

        • P is the second parameter of the binomial distribution.  The
          elements of P must be probabilities
     N and P must be of common size or one of them must be scalar

     Return values
     -------------

        • M is the mean of the binomial distribution

        • V is the variance of the binomial distribution

     Examples
     --------

          n = 1:6;
          p = 0:0.2:1;
          [m, v] = binostat (n, p)

          [m, v] = binostat (n, 0.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the binomial distribution.



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chi2stat


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 -- statistics: [M, V] = chi2stat (N)

     Compute statistics of the χ^2 distribution.

     Arguments
     ---------

        • N is the parameter of the chi-square distribution.  The
          elements of N must be positive

     Return values
     -------------

        • M is the mean of the chi-square distribution

        • V is the variance of the chi-square distribution

     Example
     -------

          n = 1:6;
          [m, v] = chi2stat (n)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the χ^2 distribution.



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evstat


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 -- statistics: [M, V] = evstat (MU, SIGMA)

     Compute statistics of the extreme value distribution.

     ‘[M, V] = evstat (MU, SIGMA)’ returns the mean and variance of the
     type 1 extreme value distribution with location parameter MU and
     scale parameter SIGMA.  The sizes of M and V are the common size of
     MU and SIGMA.  A scalar input functions as a constant matrix of the
     same size as the other inputs.

     The type 1 extreme value distribution is also known as the Gumbel
     distribution.  The version used here is suitable for modeling
     minima; the mirror image of this distribution can be used to model
     maxima by negating X.  If Y has a Weibull distribution, then ‘X =
     log (Y)’ has the type 1 extreme value distribution.

     See also: evcdf, evinv, evpdf, evrnd, evfit, evlike.


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Compute statistics of the extreme value distribution.



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expstat


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 -- statistics: [M, V] = expstat (L)

     Compute statistics of the exponential distribution.

     Arguments
     ---------

        • L is the parameter of the exponential distribution.  The
          elements of L must be positive

     Return values
     -------------

        • M is the mean of the exponential distribution

        • V is the variance of the exponential distribution

     Example
     -------

          l = 1:6;
          [m, v] = expstat (l)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.

     See also: expcdf, expfit, expinv, exprnd, expfit, explike.


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Compute statistics of the exponential distribution.



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fstat


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 -- statistics: [MN, V] = fstat (M, N)

     Compute statistics of the F distribution.

     Arguments
     ---------

        • M is the first parameter of the F distribution.  The elements
          of M must be positive

        • N is the second parameter of the F distribution.  The elements
          of N must be positive
     M and N must be of common size or one of them must be scalar

     Return values
     -------------

        • MN is the mean of the F distribution.  The mean is undefined
          for N not greater than 2

        • V is the variance of the F distribution.  The variance is
          undefined for N not greater than 4

     Examples
     --------

          m = 1:6;
          n = 5:10;
          [mn, v] = fstat (m, n)

          [mn, v] = fstat (m, 5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the F distribution.



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gamstat


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 -- statistics: [M, V] = gamstat (A, B)

     Compute statistics of the Gamma distribution.

     Arguments
     ---------

        • A is the first parameter of the gamma distribution.  A must be
          positive

        • B is the second parameter of the gamma distribution.  B must
          be positive
     A and B must be of common size or one of them must be scalar

     Return values
     -------------

        • M is the mean of the gamma distribution

        • V is the variance of the gamma distribution

     Examples
     --------

          a = 1:6;
          b = 1:0.2:2;
          [m, v] = gamstat (a, b)

          [m, v] = gamstat (a, 1.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the Gamma distribution.



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geostat


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 -- statistics: [M, V] = geostat (P)

     Compute statistics of the geometric distribution.

     Arguments
     ---------

        • P is the rate parameter of the geometric distribution.  The
          elements of P must be probabilities

     Return values
     -------------

        • M is the mean of the geometric distribution

        • V is the variance of the geometric distribution

     Example
     -------

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

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the geometric distribution.



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gevstat


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 -- statistics: [M, V] = gevstat (K, SIGMA, MU)

     Compute statistics of the generalized extreme value distribution.

     Arguments
     ---------

        • K is the shape parameter of the GEV distribution.  (Also
          denoted gamma or xi.)
        • SIGMA is the scale parameter of the GEV distribution.  The
          elements of SIGMA must be positive.
        • MU is the location parameter of the GEV distribution.
     The inputs must be of common size, or some of them must be scalar.

     Return values
     -------------

        • M is the mean of the GEV distribution

        • V is the variance of the GEV distribution

     See also: gevcdf, gevfit, gevinv, gevlike, gevpdf, gevrnd.


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Compute statistics of the generalized extreme value distribution.



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gpstat


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 -- statistics: [M, V] = gpstat (SHAPE, SCALE, LOCATION)

     Compute statistics of the generalized Pareto distribution.

     ‘[M, V] = gpstat (SHAPE, SCALE, LOCATION)’ returns the mean and
     variance of the generalized Pareto distribution with SHAPE, SCALE,
     and LOCATION parameeters.

     The default value for LOCATION is 0.

     When SHAPE = 0 and LOCATION = 0, the generalized Pareto
     distribution is equivalent to the exponential distribution.  When
     ‘SHAPE > 0’ and ‘LOCATION = SCALE / SHAPE’, the generalized Pareto
     distribution is equivalent to the Pareto distribution.  The mean of
     the generalized Pareto distribution is not finite when ‘SHAPE >=
     1’, and the variance is not finite when ‘SHAPE >= 1/2’.  When
     ‘SHAPE >= 0’, the generalized Pareto distribution has positive
     density for ‘X > LOCATION’, or, when ‘SHAPE < 0’, for ‘0 <= (X -
     LOCATION) / SCALE <= -1 / SHAPE’.

     See also: gpcdf, gpinv, gppdf, gprnd, gpfit, gplike.


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Compute statistics of the generalized Pareto distribution.



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hygestat


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 -- statistics: [MN, V] = hygestat (T, M, N)

     Compute statistics of the hypergeometric distribution.

     Arguments
     ---------

        • T is the total size of the population of the hypergeometric
          distribution.  The elements of T must be positive natural
          numbers

        • M is the number of marked items of the hypergeometric
          distribution.  The elements of M must be natural numbers

        • N is the size of the drawn sample of the hypergeometric
          distribution.  The elements of N must be positive natural
          numbers
     T, M, and N must be of common size or scalar

     Return values
     -------------

        • MN is the mean of the hypergeometric distribution

        • V is the variance of the hypergeometric distribution

     Examples
     --------

          t = 4:9;
          m = 0:5;
          n = 1:6;
          [mn, v] = hygestat (t, m, n)

          [mn, v] = hygestat (t, m, 2)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the hypergeometric distribution.



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lognstat


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 -- statistics: [M, V] = lognstat (MU, SIGMA)

     Compute statistics of the lognormal distribution.

     Arguments
     ---------

        • MU is the first parameter of the lognormal distribution

        • SIGMA is the second parameter of the lognormal distribution.
          SIGMA must be positive or zero
     MU and SIGMA must be of common size or one of them must be scalar

     Return values
     -------------

        • M is the mean of the lognormal distribution

        • V is the variance of the lognormal distribution

     Examples
     --------

          mu = 0:0.2:1;
          sigma = 0.2:0.2:1.2;
          [m, v] = lognstat (mu, sigma)

          [m, v] = lognstat (0, sigma)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the lognormal distribution.



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nbinstat


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 -- statistics: [M, V] = nbinstat (N, P)

     Compute statistics of the negative binomial distribution.

     Arguments
     ---------

        • N is the first parameter of the negative binomial
          distribution.  The elements of N must be natural numbers

        • P is the second parameter of the negative binomial
          distribution.  The elements of P must be probabilities
     N and P must be of common size or one of them must be scalar

     Return values
     -------------

        • M is the mean of the negative binomial distribution

        • V is the variance of the negative binomial distribution

     Examples
     --------

          n = 1:4;
          p = 0.2:0.2:0.8;
          [m, v] = nbinstat (n, p)

          [m, v] = nbinstat (n, 0.5)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the negative binomial distribution.



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ncfstat


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 -- statistics: [M, V] = ncfstat (DF1, DF1, DELTA)

     Compute statistics for the noncentral F distribution.

     ‘[M, V] = ncfstat (DF1, DF1, DELTA)’ returns the mean and variance
     of the noncentral F distribution with DF1 and DF2 degrees of
     freedom and noncentrality parameter DELTA.

     The size of M and V is the common size of the input arguments.
     Scalar input arguments DF1, DF2, and DELTA are regarded as constant
     matrices of the same size as the other input.

     See also: ncfcdf, ncfinv, ncfpdf, ncfrnd.


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Compute statistics for the noncentral F distribution.



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nctstat


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 -- statistics: [M, V] = nctstat (DF, DELTA)

     Compute statistics for the noncentral t distribution.

     ‘[M, V] = nctstat (DF, DELTA)’ returns the mean and variance of the
     noncentral t distribution with DF degrees of freedom and
     noncentrality parameter DELTA.

     The size of M and V is the common size of the input arguments.
     Scalar input arguments DF and DELTA are regarded as constant
     matrices of the same size as the other input.

     See also: nctcdf, nctinv, nctpdf, nctrnd.


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Compute statistics for the noncentral t distribution.



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ncx2stat


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 -- statistics: [M, V] = ncx2stat (DF, DELTA)

     Compute statistics for the noncentral χ^2 distribution.

     ‘[M, V] = ncx2stat (DF, DELTA)’ returns the mean and variance of
     the noncentral chi-square distribution with DF degrees of freedom
     and noncentrality parameter DELTA.

     The size of M and V is the common size of the input arguments.
     Scalar input arguments DF and DELTA are regarded as constant
     matrices of the same size as the other input.

     See also: ncx2cdf, ncx2inv, ncx2pdf, ncx2rnd.


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Compute statistics for the noncentral χ^2 distribution.



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normstat


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 -- statistics: [MN, V] = normstat (M, S)

     Compute statistics of the normal distribution.

     Arguments
     ---------

        • M is the mean of the normal distribution

        • S is the standard deviation of the normal distribution.  S
          must be positive
     M and S must be of common size or one of them must be scalar

     Return values
     -------------

        • MN is the mean of the normal distribution

        • V is the variance of the normal distribution

     Examples
     --------

          m = 1:6;
          s = 0:0.2:1;
          [mn, v] = normstat (m, s)

          [mn, v] = normstat (0, s)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the normal distribution.



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poisstat


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 -- statistics: [M, V] = poisstat (LAMBDA)

     Compute statistics of the Poisson distribution.

     Arguments
     ---------

        • LAMBDA is the parameter of the Poisson distribution.  The
          elements of LAMBDA must be positive

     Return values
     -------------

        • M is the mean of the Poisson distribution

        • V is the variance of the Poisson distribution

     Example
     -------

          lambda = 1 ./ (1:6);
          [m, v] = poisstat (lambda)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.

     See also: poisscdf, poissinv, poisspdf, poissrnd.


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Compute statistics of the Poisson distribution.



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raylstat


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 -- statistics: [M, V] = raylstat (SIGMA)

     Compute statistics of the Rayleigh distribution.

     Arguments
     ---------

        • SIGMA is the parameter of the Rayleigh distribution.  The
          elements of SIGMA must be positive.

     Return values
     -------------

        • M is the mean of the Rayleigh distribution.

        • V is the variance of the Rayleigh distribution.

     Example
     -------

          sigma = 1:6;
          [m, v] = raylstat (sigma)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the Rayleigh distribution.



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tstat


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 -- statistics: [M, V] = tstat (N)

     Compute statistics of the t distribution.

     Arguments
     ---------

        • N is the parameter of the t (Student) distribution.  The
          elements of N must be positive

     Return values
     -------------

        • M is the mean of the t (Student) distribution

        • V is the variance of the t (Student) distribution

     Example
     -------

          n = 3:8;
          [m, v] = tstat (n)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the t distribution.



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unidstat


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 -- statistics: [M, V] = unidstat (N)

     Compute statistics of the discrete uniform distribution.

     Arguments
     ---------

        • N is the parameter of the discrete uniform distribution.  The
          elements of N must be positive natural numbers

     Return values
     -------------

        • M is the mean of the discrete uniform distribution

        • V is the variance of the discrete uniform distribution

     Example
     -------

          n = 1:6;
          [m, v] = unidstat (n)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the discrete uniform distribution.



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unifstat


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 -- statistics: [M, V] = unifstat (A, B)

     Compute statistics of the continuous uniform distribution.

     Arguments
     ---------

        • A is the first parameter of the continuous uniform
          distribution

        • B is the second parameter of the continuous uniform
          distribution
     A and B must be of common size or one of them must be scalar and A
     must be less than B

     Return values
     -------------

        • M is the mean of the continuous uniform distribution

        • V is the variance of the continuous uniform distribution

     Examples
     --------

          a = 1:6;
          b = 2:2:12;
          [m, v] = unifstat (a, b)

          [m, v] = unifstat (a, 10)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the continuous uniform distribution.



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wblstat


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 -- statistics: [M, V] = wblstat (SCALE, SHAPE)

     Compute statistics of the Weibull distribution.

     Arguments
     ---------

        • SCALE is the scale parameter of the Weibull distribution.
          SCALE must be positive

        • SHAPE is the shape parameter of the Weibull distribution.
          SHAPE must be positive
     SCALE and SHAPE must be of common size or one of them must be
     scalar

     Return values
     -------------

        • M is the mean of the Weibull distribution

        • V is the variance of the Weibull distribution

     Examples
     --------

          scale = 3:8;
          shape = 1:6;
          [m, v] = wblstat (scale, shape)

          [m, v] = wblstat (6, shape)

     References
     ----------

       1. Wendy L. Martinez and Angel R. Martinez.  ‘Computational
          Statistics Handbook with MATLAB’. Appendix E, pages 547-557,
          Chapman & Hall/CRC, 2001.

       2. Athanasios Papoulis.  ‘Probability, Random Variables, and
          Stochastic Processes’.  McGraw-Hill, New York, second edition,
          1984.


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Compute statistics of the Weibull distribution.





