Building your first model

Installing MCHammer

Install the package as usual using Pkg.

    using Pkg
    Pkg.("MCHammer")

If you need to install direct, we recommend using ']' to go in the native Pkg manager.

    (v1.1) pkg> add https://github.com/etorkia/MCHammer.jl

Loading MCHammer

To load the MCHammer package

using MCHammer

Getting your environment setup for modeling

In order to build your first model, you will need to get a few more packages installed:

Distributions.jl : To build a simulation, you need distributions as inputs. Julia offers univariate and multivariate distributions covering most needs.
StatsBase.jl and Statistics.jl : These packages provide all the functions to analyze results and build models.

To load the support packages:

  julia> using Distributions, Statistics, StatsBase, DataFrames

Building a simple example

EVERY MONTE CARLO MODEL HAS 3 COMPONENTS

Inputs: Ranges or Single Values
A Model: Set of mathematical relationships f(x)
Outputs: The variable(s) of interest you want to analyze

Main Distributions for most modeling situations

Though the most used distributions are cite below, Julia's Distributions package has an impressive array of options. Please check out the complete library of distributions at Distributions.jl

Normal()
LogNormal()
Triangular()
Uniform()
Beta()
Exponential()
Gamma()
Weibull()
Poisson()
Binomial()
Bernoulli()

In order to define a simulated input you need to use the rand function. By assigning a variable name, you can generate any simulated vector you want.

using Distributions, Random
Random.seed!(1)
input_variable = rand(Normal(0,1),100)

100-element Vector{Float64}:
  0.06193274031408013
  0.2784058141640002
 -0.5958244153640522
  0.04665938957338174
  1.0857940215432762
 -1.5765649225859841
  0.1759399913010747
  0.8653808054093252
 -2.790281005549307
 -1.8920155582259128
  ⋮
  0.747446113596017
 -0.5200214906974596
 -0.25155469243873996
  1.219317449444866
  1.0026816589160366
  0.972024394360624
  1.546409924955377
 -0.5841980481085709
  0.46774878539798725

Creating a simple model

A model is either a visual or mathematical representation of a situation or system. The easiest example of a model is

PROFIT = REVENUE - EXPENSES

Let's create a simple simulation model with 1000 trials with the following inputs:

Setup environment and inputs

n_trials = 1000
Revenue = rand(TriangularDist(2500000,4000000,3000000), n_trials)
Expenses = rand(TriangularDist(1400000,3000000,2000000), n_trials)

1000-element Vector{Float64}:
 2.1276849954543347e6
 1.8081873781452307e6
 1.544879902357442e6
 1.8880541225801776e6
 2.5447218679510015e6
 2.162878322589141e6
 2.450585401245652e6
 2.7665033929929947e6
 2.0637354857680933e6
 2.3840473601053483e6
 ⋮
 2.1254683577667978e6
 1.8042545395649583e6
 1.8132617966068545e6
 1.9613235513769118e6
 1.8308271321740407e6
 2.342718789527916e6
 2.1114726078079096e6
 2.636000060944828e6
 2.0433610096553492e6

Define a Model and Outputs

# The Model
Profit = Revenue - Expenses

#Trial Results : the Profit vector (OUTPUT)
Profit

1000-element Vector{Float64}:
      1.3059645011598323e6
      1.54515492309168e6
      1.7176910748612264e6
 634634.3276538644
 361826.2604960487
 966992.6143540088
      1.0469871383461733e6
  99239.68692632765
 914122.4699177747
 616543.220599601
      ⋮
 765170.8771777772
      1.124483006433995e6
      1.6927099550849595e6
 925371.6289863433
      1.2103149177766917e6
 697792.9995724442
      1.3143058833978418e6
 726636.9191863816
      1.1741165929685102e6

Analyzing the results in Julia

# `fractiles()` allows you to get the percentiles at various increments.

fractiles(Profit)

11×2 Matrix{Any}:
 "P0.0"    -3.30304e5
 "P10.0"    4.72844e5
 "P20.0"    6.4124e5
 "P30.0"    7.73507e5
 "P40.0"    9.03596e5
 "P50.0"    1.02306e6
 "P60.0"    1.14913e6
 "P70.0"    1.28132e6
 "P80.0"    1.41412e6
 "P90.0"    1.63562e6
 "P100.0"   2.29578e6

density_chrt(Profit)

Sensitivity Analysis

First we need to create a sensitivity table with hcat() using both the input and output vectors.

#Construct the sensitivity input table by consolidating all the relevant inputs and outputs.

s_table = DataFrame(Profit = Profit, Revenue = Revenue, Expenses = Expenses)

#To produce a sensitivity tornado chart, we need to select the output against
#which the inputs are measured for effect.

sensitivity_chrt(s_table, 1, 3)