Phi: The Cumulative distribution function Phi(x) of the Standard...

In BayesianFROC: FROC Analysis by Bayesian Approaches

Description

Φ(x):= \int_{-∞}^x \frac{1}{√{2π}} e^{\frac{-x^2}{2}}

Usage

Phi(x)

Arguments

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

Value

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

See Also

Phi_inv()

Examples

#========================================================================================
#            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)

BayesianFROC documentation built on Jan. 23, 2022, 9:06 a.m.