fmpdistribution 1.0.0

A Python package for calculating pdf, cdf, and sf for Poisson, Binomial,Normal, Multinomial and Exponential distributions.

fmpdistribution - Package for computing probabilities for discrete and continuous random variables.

fmpdistribution package provides different functions to calculate probability and common statistics for Poisson, Binomial, Normal, Multinomial, and Exponential distributions. The package contains five classes, one for each probability distribution. Class Poisson Method Summary

Methods	Description
pdf(x,mu)	Probability Density Function
cdf(x,mu,steps=False)	Cummulative Distribution Function
sf(x,mu)	Survival Function (1-cdf)
stats(mu)	Mean, Median, Mode ,Variance, Skewness, Kurtosis
Parameters:
x: value of the poisson random variable.
mu: average number of occurrences in specific interval.
steps: shows all probabilities from 0 to x when it is True.

Class Binomial Method Summary

Methods	Description
pdf(x,n,p)	Probability Density Function
cdf(x,n,p,steps=False)	Cummulative Distribution Function
sf(x,n,p)	Survival Function (1-cdf)
stats(n,p)	Mean, Median, Mode ,Variance, Skewness, Kurtosis
Parameters:
x: value of the binomial random variable.
n: number of trials.
p: probability of success.
steps: shows all probabilities from 0 to x when it is True.

Class Normal Method Summary

Methods	Description
pdf(x,mu=0,sd=1)	Probability Density Function
cdf(x,mu=0,sd=1)	Cummulative Distribution Function
sf(x,mu=0,sd=1)	Survival Function (1-cdf)
stats(mu=0,sd=1)	Mean, Median, Mode ,Variance, Skewness, Kurtosis
Parameters:
x: value of the normal random variable.
mu: mean of the normal distribution.
sd: standard deviation of the normal distribution.

Class Exponential Method Summary

Methods	Description
pdf(x,mu)	Probability density function
cdf(x,mu)	Probability distribution function
sf(x,mu)	Survival function (1-cdf)
stats(x,mu)	Mean, Median, Mode ,Variance, Skewness, Kurtosis
Parameters:
x: value of random variable follows exponential distribution.
mu: average number of occurrences.

Class Multinomial Method Summary

Methods	Description
pdf(n,outcomes,prob)	Probability density function
stats(n,outcomes,prob)	Mean, Variance
cov(n,outcomes,prob)	Covariance
Parameters:
n: total number of events.
outcomes: number of occurrences of each event.
prob: probability of each event.

Dependencies:

• No external package is required

Installation:

In oder to compute probabilities, we must install fmpdistribution . Use the package installer (PIP) or package management system (conda) to install fmpdistribution.

 pip install fmpdistribution
 python -m pip install fmpdistribution
 conda install fmpdistribution 

How to use:

import the probability distribution calss from fmpdistribution
call the required function
provide input 
execute the code

####Example-1: A person receives on average 3 emails per hour. What the probability that he will receive (a) 4 emails in the next hour (b) Less than or equal to 4 (c) Greater than 4

Solution:

    from fmpdistribution.Poisson import Poisson
    pp = Poisson()
    mu = 3
    print(pp.pdf(4,mu))    # P(X=4)
    0.168031
     print(pp.cdf(4,mu))   # P(X<=4)
    0.815263
    print(pp.sf(4,mu))      # P(X>4)
    or print(1-pp.cdf(4,mu))
    0.184736
    #To get common statistics:
    print(pp.stats(mu))
    {'mean': 3, 'median': 3.326667, 'mode': 3, 'variance': 3, 'skewnes': 0.577350, 'kurtosis': 0.333333} 

####Example-2: In a computer science class 40% students belong to Asia, 50% to Europe and 10% to USA. If we select a random sample of 10 students, what is the probability that 3 candidates from Asia, 5 from Europe and 2 from USA?

Solution:

 from fmpdistribution.Multinomial import Multinomial
 import numpy as np`
 mn = Multinomial()
 n = 10
 x = [3,5,2]
 p = [0.40,0.50,0.10]
 print(mn.pdf(n,x,p)) # probability density function
 print(np.array(mn.cov(n,p)))  # covariance
	
0.050400
[[ 2.4 -2.  -0.4]
 [-2.   2.5 -0.5]
 [-0.4 -0.5  0.9]]

Version History

1.0.0 (Initial release)

License

This project is licensed under the MIT License - see the LICENSE.txt file for details