# How to plot this step-wise function?

I have a step-wise function. It is a function with theta.

If the question is about plotting, a representative data set is needed. If it's about creating the data frame, do you mean \beta_{i\dots n}, etc? Otherwise, what are P_\theta and X_1?

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There is no data. Just plot this function. No restriction of theta. Theta is from negative infinity to positive infinity. And the range is from 0 to 1.

Please ignore P_θ. The function is called \beta_1, in terms of \theta.

Still not sure of your intent. Also assumed that the third condition was 0.95 >

theta <- seq(-0.05,0.95,.01)
eq <- function(x) dplyr::case_when(
x <= -0.05 ~ 0,
x > 0.05 & x <= 0.95 ~ x + 0.05,
x > 0.95 ~ 1
)

plot(eq(theta), type = 'l')


plot(eq(sample(theta,500, replace = TRUE)), type = 'l')


When x <= -0.05, f(x)=0
When -0.05<x <=0.95, then f(x)=x+0.05
When x>0.95, f(x)=1

Please plot the curve of f(x).

If

eq <- function(x) dplyr::case_when(
x <= -0.05 ~ 0,
x > 0.05 & x <= 0.95 ~ x + 0.05,
x > 0.95 ~ 1
)


isn't what you intended, provide a replacement.

One way to generate data explicitly in a bounded interval and plot the function.

library(tidyverse)
x<-seq(-2,2, 0.025)
fx_gen<-function(x){
fx<-1
if(x <= -0.05){
fx<-0
}else if(-0.05<x & x<=0.95){
fx<-x+0.05
}
return(fx)
}
fx<-map_dbl(x, ~fx_gen(.x))
plot(x,fx,type = "l")


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