benluiwj / ST2334-Distributions

Based on the word document given by the lecturer, I converted the commands into a CLI in python.

ST2334-Distributions

Based on the word document given by the lecturer, I converted the commands into a CLI in python.

To run

1. Ensure that you have scipy installed in your python environment.
2. Run python3 statistic commands.py

Help list

Distributions Available

• Binomial Distribution
• Normal Binomial Distribution
• Poisson Distribution
• Exponential Distribution
• Normal Distribution
• Continuous Variable (represented by T)
• Chi Squared Continuous Random Variable (represented by Chisq)
• F Continuous Random Variable (represented by F)

Commands Available

Binomial Distribution

Let the base be X ~ B(trials, probability of success)

• cdf(number of successes) : Calculates Pr(X <= number of successes)
• pmf(number of successes) : Calculates Pr(X = number of successes)
• greater_than(number of successors) : Calculates Pr(X > number of successes)
• ppf(probability) : Calculates Pr(X <= x) >= probability

Normal Binomial Distrbution

Let the base be X ~ NB(number of successes, probability of success)

• cdf(number of failures) : Calculates Pr(X <= number of failures)
• pmf(number of failures) : Calculates Pr(X = number of failures)
• greater_than(number of failures) : Calculates Pr(X > number of failures)
• ppf(probability) : Calculates Pr(X <= x) >= probability

Poisson Distrbution

Let the base be X ~ P(lambda value), where E(X) = lambda value

• cdf(value) : Calculates Pr(X <= value)
• pmf(value) : Calculates Pr(X = value)
• greater_than(value) : Calculates Pr(X > value)
• ppf(probability) : Calculates Pr(X <= x) >= probability

Exponential Distrbution

Let the base be X ~ Exp(lambda value), where E(X) = 1/lambda value. Note that the default lower limit is 0 for this distribution.

• cdf(value) : Calculates Pr(X <= value)
• pmf(value) : Calculates Pr(X = value)
• greater_than(value) : Calculates Pr(X > value)
• ppf(probability) : Calculates Pr(X <= x) >= probability

Normal Distrbution

Let the base be X ~ N(mu, variance), where E(X) = mu and sigma^2 = variance

• cdf(value) : Calculates Pr(X <= value)
• pmf(value) : Calculates pdf f(value)
• greater_than(value) : Calculates Pr(X > value)
• ppf_leq(probability) : Calculates Pr(X <= x) = probability
• ppf_geq(probability) : Calculates Pr(X >= x) = probability

Continuous Variable

Let the base be X ~ t(degree of freedom)

• cdf(value) : Calculates Pr(X <= value)
• pmf(value) : Calculates pdf f(value)
• greater_than(value) : Calculates Pr(X > value)
• ppf_leq(probability) : Calculates Pr(X <= x) = probability
• ppf_geq(probability) : Calculates Pr(X >= x) = probability

Chi Squared Continuous Random Variable

Let the base be X ~ Chisq(degree of freedom)

• cdf(value) : Calculates Pr(X <= value)
• pmf(value) : Calculates pdf f(value)
• greater_than(value) : Calculates Pr(X > value)
• ppf_leq(probability) : Calculates Pr(X <= x) = probability
• ppf_geq(probability) : Calculates Pr(X >= x) = probability

F Continuous Random Variable

Let the base be X ~ F(freedom1, freedom2)

• cdf(value) : Calculates Pr(X <= value)
• pmf(value) : Calculates pdf f(value)
• greater_than(value) : Calculates Pr(X > value)
• ppf_leq(probability) : Calculates Pr(X <= x) = probability
• ppf_geq(probability) : Calculates Pr(X >= x) = probability