BayesianFROC (version 1.0.0)

Phi: The Cumulative distribution function \(\Phi(x)\) of the Standard Gaussian, namely, mean = 0 and variance =1.

Description

$$\Phi(x):= \int_{-\infty}^x \frac{1}{\sqrt{2\pi}} e^{\frac{-x^2}{2}} $$

Usage

Phi(x)

Arguments

x

A real. To be passed to the function stats::pnorm()

Value

\(\Phi(x) := \int _{-\infty}^x Gaussian(z|0,1)dz \)

See Also

Phi_inv()

Examples

# NOT RUN {
#========================================================================================
#            1)             validation of this function
#========================================================================================
#'
  x<-0.2
 Phi(x)==stats::pnorm(x)



#========================================================================================
#            1)             Build the data
#========================================================================================
#'

 a  <-  0.1;
 NX <-  222;
 x  <-  runif(100,-11,11)
 y  <-  Phi_inv(exp(a/NX) *Phi(x))-x
 plot(x,y)

 a  <-  0.1;
 NX <-  222;
 x  <-  runif(100,0,11)
 y  <-  Phi_inv(exp(a/NX) *Phi(x))-x
 plot(x,y)


 a  <-  0.1;
 NX <-  222;
 x  <-  runif(100,2,4)
 y  <-  Phi_inv(exp(a/NX) *Phi(x))-x
 plot(x,y)

 a  <-  0.01;
 NX <-  222;
 x  <-  runif(100,2,4);
 y  <-  Phi_inv(exp(a/NX) *Phi(x))-x
 plot(x,y)




 a  <-  0.01;
 NX <-  222;
 x  <-  runif(100,3.5,4);
 y  <-  Phi_inv(exp(a/NX) *Phi(x))-x
 plot(x,y)


# }