How to resolve the algorithm Statistics/Normal distribution step by step in the Stata programming language

Published on 12 May 2024 09:40 PM
#Stata

How to resolve the algorithm Statistics/Normal distribution step by step in the Stata programming language

Table of Contents

Problem Statement

The Normal (or Gaussian) distribution is a frequently used distribution in statistics. While most programming languages provide a uniformly distributed random number generator, one can derive normally distributed random numbers from a uniform generator.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Statistics/Normal distribution step by step in the Stata programming language

Source code in the stata programming language

clear all
set obs 100000
gen u=runiform()
gen v=runiform()
gen r=sqrt(-2*log(u))
gen x=r*cos(2*_pi*v)
gen y=r*sin(2*_pi*v)
gen z=rnormal()
sum x y z

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
           x |    100,000    .0025861    1.002346  -4.508192   4.164336
           y |    100,000    .0017389    1.001586  -4.631144   4.460274
           z |    100,000     .005054    .9998861  -5.134265   4.449522
hist x, normal
hist y, normal
hist z, normal
qqplot x z, msize(tiny)

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