Normdf

Normdf

Purpose

Normal / Gaussian distribution.

Synopsis

prob = normdf(function,x,a,b)

Description

Estimates cumulative distribution function (cumulative, cdf), probability density function (density, pdf), quantile (inverse of cdf), or random numbers for a Normal distribution.

This distribution is used for many data types including physical attributes and sums of quantities. It is a symmetric distribution and the variance can be smaller, equal, or larger than the mean.

$f(x)= \frac {1} {b \left ( 2 \pi \right ) ^ {1/2}} \exp \left [ \frac {- \left ( x -a \right )^2} {2b^2} \right ]$

Inputs

• function = [ {'cumulative'} | 'density' | 'quantile' | 'random' ], defines the functionality to be used. Note that the function recognizes the first letter of each string so that the string could be: [ 'c' | 'd' | 'q' | 'r' ].

• x = matrix in which the sample data is stored, in the interval (-inf,inf).

for function=quantile - matrix with values in the interval (0,1).

for function=random - vector indicating the size of the random matrix to create.

• a = mode/location parameter (real).

• b = scale parameter (real and positive).

Note: If inputs (x, a, and b) are not equal in size, the function will attempt to resize all inputs to the largest input using the RESIZE function.

Note: Functions will typically allow input values outside of the acceptable range to be passed but such values will return NaN in the results.

Examples

Cumulative

>> prob = normdf('c',[1.9600 2.5758])
ans =
    0.9750    0.9950
>> x = -5:.1:5;
>> plot(x,normdf('c',x,0,1)), vline([ 0 ; normdf('q',[0.975; 0.995],0,1)])

Density

>> prob = normdf('d',[1.9600 2.5758],0,1)
ans =
    0.0584    0.0145
>> x = -5:.1:5;
>> plot(x,normdf('d',x,0,1)), vline([0; normdf('q',[0.975; 0.995],0,1)])

Quantile

>> prob = normdf('q',[.975 .995],0,1)
ans =
    1.9600    2.5758

Random

>> prob = normdf('r',[4 1],0,1)
ans =
   -0.4326
   -1.6656
    0.1253
    0.2877

See Also

betadf, cauchydf, chidf, expdf, gammadf, gumbeldf, laplacedf, logisdf, lognormdf, paretodf, raydf, triangledf, unifdf, weibulldf