R_Functions.py

"""
Compact Python wrapper library for commonly used R-style functions
============================================================================
Basic functional programming nature of R provides users with extremely simple and compact interface for quick calculations of probabilities and essential descriptive/inferential statistics for a data analysis problem. On the other hand, Python scripting ability allows the analyst to use those statistics in a wide variety of analytics pipeline with limitless sophistication and creativity. To combine the advantage of both worlds, one needs a simple Python-based wrapper library which contains some basic functions pertaining to probability distributions and descriptive statistics defined in R-style so that users can call those functions fast without having to go to the proper Python statistical libraries and figure out the whole list of methods and arguments.

Goal of this library is to provide simple Python sub-routines mimicing R-style statistical functions for quickly calculating density/point estimates, cumulative distributions, quantiles, and generating random variates for various important probability distributions. To maintain the spirit of R styling, no class hiararchy was used and just raw functions are defined in this file so that user can import this one Python script and use all the functions whenever he/she needs them with a single name call.
"""

#============================
Basic Descriptive Statistics
#============================

def mean(array):
    """
    Calculates the mean of an array/vector
    """
    import numpy as np
    array=np.array(array)
    result= np.mean(array)
    return result

def sd(array):
    """
    Calculates the standard deviation of an array/vector
    """
    import numpy as np
    array=np.array(array)
    result= np.std(array)
    return result

def median(array):
    """
    Calculates the median of an array/vector
    """
    import numpy as np
    array=np.array(array)
    result= np.median(array)
    return result

def var(array):
    """
    Calculates the variance of an array/vector
    """
    import numpy as np
    array=np.array(array)
    result= np.var(array)
    return result

def cov(x,y=None):
    """
    Calculates the covariance between two arrays/vectors or of a single matrix
    """
    import numpy as np
    array1=np.array(x)
    if y!=None:
        array2=np.array(y)
        if array1.shape!=array2.shape:
            print("Error: incompatible dimensions")
            return None
        covmat=np.cov(array1,array2)
        result=covmat[0][1]
    elif len(array1.shape)==1:
        result=float(np.cov(array1))
    else:
        result=np.cov(array1)
    return result        

def fivenum(array):
    """
    Calculates the Tuckey Five-number (min/median/max/1st quartile/3rd quartile) of an array/vector
    """
    import numpy as np
    array=np.array(array)
    result=[0]*5
    result[0]=np.min(array)
    result[1]=np.percentile(array,25)
    result[2]=np.median(array)
    result[3]=np.percentile(array,75)
    result[4]=np.max(array)
    result=np.array(result)
    
    return result

def IQR(array):
    """
    Calculates the inter-quartile range of an array/vector
    """
    import numpy as np
    array=np.array(array)
    result = np.percentile(array,75)-np.percentile(array,25)
    
    return result

"""
Probability distributions
"""

#=====================
# Uniform distribution
#=====================

def dunif(x, minimum=0,maximum=1):
    """
    Calculates the point estimate of the uniform distribution
    """
    from scipy.stats import uniform
    result=uniform.pdf(x=x,loc=minimum,scale=maximum-minimum)
    return result

def punif(q, minimum=0,maximum=1):
    """
    Calculates the cumulative of the uniform distribution
    """
    from scipy.stats import uniform
    result=uniform.cdf(x=q,loc=minimum,scale=maximum-minimum)
    return result

def qunif(p, minimum=0,maximum=1):
    """
    Calculates the quantile function of the uniform distribution
    """
    from scipy.stats import uniform
    result=uniform.ppf(q=p,loc=minimum,scale=maximum-minimum)
    return result

def runif(n, minimum=0,maximum=1):
    """
    Generates random variables from the uniform distribution
    """
    from scipy.stats import uniform
    result=uniform.rvs(size=n,loc=minimum,scale=maximum-minimum)
    return result

#======================
# Binomial distribution
#======================

def dbinom(x,size,prob=0.5):
    """
    Calculates the point estimate of the binomial distribution
    """
    from scipy.stats import binom
    result=binom.pmf(k=x,n=size,p=prob,loc=0)
    return result

def pbinom(q,size,prob=0.5):
    """
    Calculates the cumulative of the binomial distribution
    """
    from scipy.stats import binom
    result=binom.cdf(k=q,n=size,p=prob,loc=0)
    return result

def qbinom(p, size, prob=0.5):
    """
    Calculates the quantile function from the binomial distribution
    """
    from scipy.stats import binom
    result=binom.ppf(q=p,n=size,p=prob,loc=0)
    return result

def rbinom(n,size,prob=0.5):
    """
    Generates random variables from the binomial distribution
    """
    from scipy.stats import binom
    result=binom.rvs(n=size,p=prob,size=n)
    return result

#=====================
# Normal distribution
#=====================

def dnorm(x,mean=0,sd =1):
    """
    Calculates the density of the Normal distribution
    """
    from scipy.stats import norm
    result=norm.pdf(x,loc=mean,scale=sd)
    return result

def pnorm(q,mean=0,sd=1):
    """
    Calculates the cumulative of the normal distribution
    """
    from scipy.stats import norm
    result=norm.cdf(x=q,loc=mean,scale=sd)
    return result

def qnorm(p,mean=0,sd=1):
    """
    Calculates the quantile function of the normal distribution
    """
    from scipy.stats import norm
    result=norm.ppf(q=p,loc=mean,scale=sd)
    return result

def rnorm(n,mean=0,sd=1):
    """
    Generates random variables from the normal distribution
    """
    from scipy.stats import norm
    result=norm.rvs(size=n,loc=mean,scale=sd)
    return result

#=====================
# Poisson distribution
#=====================

def dpois(x,mu):
    """
    Calculates the density/point estimate of the Poisson distribution
    """
    from scipy.stats import poisson
    result=poisson.pmf(k=x,mu=mu)
    return result

def ppois(q,mu):
    """
    Calculates the cumulative of the Poisson distribution
    """
    from scipy.stats import poisson
    result=poisson.cdf(k=q,mu=mu)
    return result

def qpois(p,mu):
    """
    Calculates the quantile function of the Poisson distribution
    """
    from scipy.stats import poisson
    result=poisson.ppf(q=p,mu=mu)
    return result

def rpois(n,mu):
    """
    Generates random variables from the Poisson distribution
    """
    from scipy.stats import poisson
    result=poisson.rvs(size=n,mu=mu)
    return result

#=====================
# chi^2-distribution
#=====================

def dchisq(x,df,ncp=0):
    """
    Calculates the density/point estimate of the chi-square distribution
    """
    from scipy.stats import chi2,ncx2
    if ncp==0:
        result=chi2.pdf(x=x,df=df,loc=0,scale=1)
    else:
        result=ncx2.pdf(x=x,df=df,nc=ncp,loc=0,scale=1)
    return result

def pchisq(q,df,ncp=0):
    """
    Calculates the cumulative of the chi-square distribution
    """
    from scipy.stats import chi2,ncx2
    if ncp==0:
        result=chi2.cdf(x=q,df=df,loc=0,scale=1)
    else:
        result=ncx2.cdf(x=q,df=df,nc=ncp,loc=0,scale=1)
    return result

def qchisq(p,df,ncp=0):
    """
    Calculates the quantile function of the chi-square distribution
    """
    from scipy.stats import chi2,ncx2
    if ncp==0:
        result=chi2.ppf(q=p,df=df,loc=0,scale=1)
    else:
        result=ncx2.ppf(q=p,df=df,nc=ncp,loc=0,scale=1)
    return result

def rchisq(n,df,ncp=0):
    """
    Generates random variables from the chi-square distribution
    """
    from scipy.stats import chi2,ncx2
    if ncp==0:
        result=chi2.rvs(size=n,df=df,loc=0,scale=1)
    else:
        result=ncx2.rvs(size=n,df=df,nc=ncp,loc=0,scale=1)
    return result

#==============================
# ### Student's t-distribution
#==============================

def dt(x,df,ncp=0):
    """
    Calculates the density/point estimate of the t-distribution
    """
    from scipy.stats import t,nct
    if ncp==0:
        result=t.pdf(x=x,df=df,loc=0,scale=1)
    else:
        result=nct.pdf(x=x,df=df,nc=ncp,loc=0,scale=1)
    return result

def pt(q,df,ncp=0):
    """
    Calculates the cumulative of the t-distribution
    """
    from scipy.stats import t,nct
    if ncp==0:
        result=t.cdf(x=q,df=df,loc=0,scale=1)
    else:
        result=nct.cdf(x=q,df=df,nc=ncp,loc=0,scale=1)
    return result

def qt(p,df,ncp=0):
    """
    Calculates the quantile function of the t-distribution
    """
    from scipy.stats import t,nct
    if ncp==0:
        result=t.ppf(q=p,df=df,loc=0,scale=1)
    else:
        result=nct.ppf(q=p,df=df,nc=ncp,loc=0,scale=1)
    return result

def rt(n,df,ncp=0):
    """
    Generates random variables from the t-distribution
    """
    from scipy.stats import t,nct
    if ncp==0:
        result=t.rvs(size=n,df=df,loc=0,scale=1)
    else:
        result=nct.rvs(size=n,df=df,nc=ncp,loc=0,scale=1)
    return result

#================
# F-distribution
#================

def df(x,df1,df2,ncp=0):
    """
    Calculates the density/point estimate of the F-distribution
    """
    from scipy.stats import f,ncf
    if ncp==0:
        result=f.pdf(x=x,dfn=df1,dfd=df2,loc=0,scale=1)
    else:
        result=ncf.pdf(x=x,dfn=df1,dfd=df2,nc=ncp,loc=0,scale=1)
    return result

def pf(q,df1,df2,ncp=0):
    """
    Calculates the cumulative of the F-distribution
    """
    from scipy.stats import f,ncf
    if ncp==0:
        result=f.cdf(x=q,dfn=df1,dfd=df2,loc=0,scale=1)
    else:
        result=ncf.cdf(x=q,dfn=df1,dfd=df2,nc=ncp,loc=0,scale=1)
    return result

def qf(p,df1,df2,ncp=0):
    """
    Calculates the quantile function of the F-distribution
    """
    from scipy.stats import f,ncf
    if ncp==0:
        result=f.ppf(q=p,dfn=df1,dfd=df2,loc=0,scale=1)
    else:
        result=ncf.ppf(q=p,dfn=df1,dfd=df2,nc=ncp,loc=0,scale=1)
    return result

def rf(n,df1,df2,ncp=0):
    """
    Calculates the quantile function of the F-distribution
    """
    from scipy.stats import f,ncf
    if ncp==0:
        result=f.rvs(size=n,dfn=df1,dfd=df2,loc=0,scale=1)
    else:
        result=ncf.rvs(size=n,dfn=df1,dfd=df2,nc=ncp,loc=0,scale=1)
    return result

#===================
# Beta distribution
#===================

def dbeta(x,shape1,shape2):
    """
    Calculates the density/point estimate of the Beta-distribution
    """
    from scipy.stats import beta
    result=beta.pdf(x=x,a=shape1,b=shape2,loc=0,scale=1)
    return result

def pbeta(q,shape1,shape2):
    """
    Calculates the cumulative of the Beta-distribution
    """
    from scipy.stats import beta
    result=beta.cdf(x=q,a=shape1,b=shape2,loc=0,scale=1)
    return result

def qbeta(p,shape1,shape2):
    """
    Calculates the cumulative of the Beta-distribution
    """
    from scipy.stats import beta
    result=beta.ppf(q=p,a=shape1,b=shape2,loc=0,scale=1)
    return result

def rbeta(n,shape1,shape2):
    """
    Calculates the cumulative of the Beta-distribution
    """
    from scipy.stats import beta
    result=beta.rvs(size=n,a=shape1,b=shape2,loc=0,scale=1)
    return result

#========================
# ### Gamma distribution
#========================

def dgamma(x,shape,rate=1):
    """
    Calculates the density/point estimate of the Gamma-distribution
    """
    from scipy.stats import gamma
    result=rate*gamma.pdf(x=rate*x,a=shape,loc=0,scale=1)
    return result

def pgamma(q,shape,rate=1):
    """
    Calculates the cumulative of the Gamma-distribution
    """
    from scipy.stats import gamma
    result=gamma.cdf(x=rate*q,a=shape,loc=0,scale=1)
    return result

def qgamma(p,shape,rate=1):
    """
    Calculates the cumulative of the Gamma-distribution
    """
    from scipy.stats import gamma
    result=(1/rate)*gamma.ppf(q=p,a=shape,loc=0,scale=1)
    return result

def rgamma(n,shape,rate=1):
    """
    Calculates the cumulative of the Gamma-distribution
    """
    from scipy.stats import gamma
    result=gamma.rvs(size=n,a=shape,loc=0,scale=1)
    return result