Normal distribution

Distribution function and quantile function of the normal distribution.

cdfnor(x, para = c(0, 1))
quanor(f, para = c(0, 1))

Arguments

x

Vector of quantiles.

f

Vector of probabilities.

para

Numeric vector containing the parameters of the distribution, in the order \(\mu, \sigma\) (location, scale).

Details

The normal distribution with location parameter \(\mu\) and scale parameter \(\sigma\) has probability density function $$f(x)={1\over \sigma\sqrt{2\pi}} \exp\lbrace-(x-\mu)^2/(2 \sigma^2)\rbrace.$$

Value

cdfnor gives the distribution function; quanor gives the quantile function.

Note

The functions expect the distribution parameters in a vector, rather than as separate arguments as in the standard R distribution functions pnorm and qnorm.

See also

pnorm for the standard R version of the normal distribution.

cdfgno for the generalized normal distribution, which generalizes the normal distribution.

Examples

# Random sample from the normal distribution
# with mean 0 and standard deviation 3.
quanor(runif(100), c(0,3))
#>   [1] -1.97821047 -0.16862920  1.61184956 -7.29633294  2.24040920 -1.87675524
#>   [7]  5.68895127 -2.62788849 -6.18021224  0.85655899  0.19363159  1.03154673
#>  [13] -0.79544218 -2.80530190 -1.34203358  0.87518778 -4.23210274  0.14339088
#>  [19] -1.51925666  1.33130788 -0.80928553  2.00320151 -3.25546478 -0.93739921
#>  [25]  1.08647735  7.57128592 -1.00701642 -1.25913089  4.09141340  4.01158239
#>  [31] -2.13457240 -0.66967674  1.98653636  1.77936876  0.87339067 -0.19580205
#>  [37]  0.59387401 -2.10355559 -3.61069834 -1.58750248 -0.11945112  0.50932395
#>  [43]  2.06094738  0.34233404  2.11580107 -2.38850126  2.97432507 -0.70814908
#>  [49]  3.43274691  3.55750912 -3.71673077  0.56386756  7.96469374  3.11642984
#>  [55] -0.47075158 -1.34937840 -1.27047031 -2.12592133 -0.59516115  0.09128165
#>  [61] -2.68440717 -1.34962305  2.71280738  2.01157110  0.23894761  5.30765828
#>  [67] -3.77648168  1.90350874  3.07705531  1.10541128 -2.19233581  4.14044607
#>  [73] -0.57043652 -2.60130115  1.58659402  7.30888479  1.65063157  0.13152849
#>  [79]  1.64905300 -0.95480676 -1.97862718  8.06595405  0.17226509  1.71131178
#>  [85] -8.42403219 -1.63419734 -2.73677922 -0.70121632 -2.34713748 -4.39759201
#>  [91] -1.99231476  1.17607006  1.87892927  2.71778542 -1.52174461  3.60490586
#>  [97]  0.81108396  3.54029081  1.40243062 -3.20156151