Statistics: normcdf

### Function Reference: `normcdf`

statistics: p = normcdf (x)
statistics: p = normcdf (x, mu)
statistics: p = normcdf (x, mu, sigma)
statistics: p = normcdf (…, `"upper"`)
statistics: [p, plo, pup] = normcdf (x, mu, sigma, pcov)
statistics: [p, plo, pup] = normcdf (x, mu, sigma, pcov, alpha)
statistics: [p, plo, pup] = normcdf (…, `"upper"`)

Normal cumulative distribution function (CDF).

For each element of x, compute the cumulative distribution function (CDF) of the normal distribution with mean mu and standard deviation sigma. The size of p is the common size of x, mu and sigma. A scalar input functions as a constant matrix of the same size as the other inputs.

Default values are mu = 0, sigma = 1.

When called with three output arguments, i.e. `[p, plo, pup]`, `normcdf` computes the confidence bounds for p when the input parameters mu and sigma are estimates. In such case, pcov, a 2×2 matrix containing the covariance matrix of the estimated parameters, is necessary. Optionally, alpha, which has a default value of 0.05, specifies the `100 * (1 - alpha)` percent confidence bounds. plo and pup are arrays of the same size as p containing the lower and upper confidence bounds.

`[…] = normcdf (…, "upper")` computes the upper tail probability of the normal distribution with parameters mu and sigma, at the values in x. This can be used to compute a right-tailed p-value. To compute a two-tailed p-value, use `2 * normcdf (-abs (x), mu, sigma)`.

Further information about the normal distribution can be found at https://en.wikipedia.org/wiki/Normal_distribution

See also: norminv, normpdf, normrnd, normfit, normlike, normstat

Source Code: normcdf

### Example: 1

     ## Plot various CDFs from the normal distribution
     x = -5:0.01:5;
     p1 = normcdf (x, 0, 0.5);
     p2 = normcdf (x, 0, 1);
     p3 = normcdf (x, 0, 2);
     p4 = normcdf (x, -2, 0.8);
     plot (x, p1, "-b", x, p2, "-g", x, p3, "-r", x, p4, "-c")
     grid on
     xlim ([-5, 5])
     legend ({"μ = 0, σ = 0.5", "μ = 0, σ = 1", ...
              "μ = 0, σ = 2", "μ = -2, σ = 0.8"}, "location", "southeast")
     title ("Normal CDF")
     xlabel ("values in x")
     ylabel ("probability")