## 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
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"description": "## fmpdistribution - Package for computing probabilities for discrete and continuous random variables.\r\n**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. \r\n***Class Poisson***\r\n\r\n**Method Summary**\r\n| **Methods** |**Description** |\r\n| ------------ | ------------ |\r\n| **pdf(x,mu)** |Probability Density Function |\r\n| **cdf(x,mu,steps=False)** |Cummulative Distribution Function |\r\n| **sf(x,mu)** |Survival Function (1-cdf) |\r\n| **stats(mu)** | Mean, Median, Mode ,Variance, Skewness, Kurtosis |\r\n**Parameters**:\r\n**x**: value of the poisson random variable. \r\n**mu**: average number of occurrences in specific interval.\r\n**steps**: shows all probabilities from 0 to x when it is True.\r\n\r\n***Class Binomial***\r\n\r\n**Method Summary**\r\n| **Methods** |**Description** |\r\n| ------------ | ------------ |\r\n| **pdf(x,n,p)** |Probability Density Function |\r\n| **cdf(x,n,p,steps=False)** | Cummulative Distribution Function |\r\n| **sf(x,n,p)** | Survival Function (1-cdf) |\r\n| **stats(n,p)** |Mean, Median, Mode ,Variance, Skewness, Kurtosis |\r\n**Parameters**:\r\n**x**: value of the binomial random variable.\r\n**n**: number of trials.\r\n**p**: probability of success.\r\n**steps**: shows all probabilities from 0 to x when it is True.\r\n\r\n***Class Normal***\r\n\r\n**Method Summary**\r\n| **Methods** |**Description** |\r\n| ------------ | ------------ |\r\n| **pdf(x,mu=0,sd=1)** |Probability Density Function |\r\n| **cdf(x,mu=0,sd=1)** | Cummulative Distribution Function |\r\n| **sf(x,mu=0,sd=1)** | Survival Function (1-cdf) |\r\n| **stats(mu=0,sd=1)** | Mean, Median, Mode ,Variance, Skewness, Kurtosis |\r\n**Parameters**:\r\n**x**: value of the normal random variable.\r\n**mu**: mean of the normal distribution.\r\n**sd**: standard deviation of the normal distribution.\r\n\r\n***Class Exponential***\r\n\r\n**Method Summary**\r\n| **Methods** |**Description** |\r\n| ------------ | ------------ |\r\n| **pdf(x,mu)** |Probability density function |\r\n| **cdf(x,mu)** | Probability distribution function |\r\n| **sf(x,mu)** | Survival function (1-cdf) |\r\n| **stats(x,mu)** |Mean, Median, Mode ,Variance, Skewness, Kurtosis |\r\n**Parameters**:\r\n**x**: value of random variable follows exponential distribution.\r\n**mu**: average number of occurrences.\r\n\r\n***Class Multinomial***\r\n\r\n**Method Summary**\r\n| **Methods** |**Description** |\r\n| ------------ | ------------ |\r\n| **pdf(n,outcomes,prob)** |Probability density function |\r\n|**stats(n,outcomes,prob)** | Mean, Variance |\r\n| **cov(n,outcomes,prob)** | Covariance |\r\n**Parameters**:\r\n**n**: total number of events.\r\n**outcomes**: number of occurrences of each event.\r\n**prob**: probability of each event.\r\n#### Dependencies:\r\n- No external package is required\r\n\r\n#### Installation:\r\nIn oder to compute probabilities, we must install **fmpdistribution** . Use the package installer (**PIP**) or package management system (**conda**) to install **fmpdistribution**.\r\n\r\n pip install fmpdistribution\r\n python -m pip install fmpdistribution\r\n conda install fmpdistribution \r\n#### How to use:\r\n import the probability distribution calss from fmpdistribution\r\n\tcall the required function\r\n provide input \r\n execute the code\r\n\r\n####Example-1:\r\nA person receives on average 3 emails per hour. What the probability that he will receive\r\n(a) 4 emails in the next hour\r\n(b) Less than or equal to 4\r\n(c) Greater than 4\r\n#### Solution:\r\n from fmpdistribution.Poisson import Poisson\r\n pp = Poisson()\r\n mu = 3\r\n print(pp.pdf(4,mu)) # P(X=4)\r\n 0.168031\r\n print(pp.cdf(4,mu)) # P(X<=4)\r\n 0.815263\r\n print(pp.sf(4,mu)) # P(X>4)\r\n or print(1-pp.cdf(4,mu))\r\n 0.184736\r\n #To get common statistics:\r\n print(pp.stats(mu))\r\n {'mean': 3, 'median': 3.326667, 'mode': 3, 'variance': 3, 'skewnes': 0.577350, 'kurtosis': 0.333333} \r\n####Example-2:\r\nIn 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?\r\n\r\n**Solution**:\r\n\r\n from fmpdistribution.Multinomial import Multinomial\r\n import numpy as np`\r\n mn = Multinomial()\r\n n = 10\r\n x = [3,5,2]\r\n p = [0.40,0.50,0.10]\r\n print(mn.pdf(n,x,p)) # probability density function\r\n print(np.array(mn.cov(n,p))) # covariance\r\n\t\t\r\n 0.050400\r\n [[ 2.4 -2. -0.4]\r\n [-2. 2.5 -0.5]\r\n [-0.4 -0.5 0.9]]\r\n\r\n#### Version History\r\n1.0.0 (Initial release)\r\n\r\n#### License\r\nThis project is licensed under the **MIT** License - see the LICENSE.txt file for details\r\n",
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