Coefficient of Variation(CV) DEMO

使用Python进行概率实验与数据可视化

最新推荐文章于 2025-02-11 16:02:16 发布

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最新推荐文章于 2025-02-11 16:02:16 发布

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#quote from MIT 'introduction to computation and programming using python, Revised'
import random
import pylab
    
def stdDev(X):
    """Assumes that X is a list of numbers.
       Returns the standard deviation of X"""
    mean = float(sum(X))/len(X)
    tot = 0.0
    for x in X:
        tot += (x - mean)**2
    return (tot/len(X))**0.5 #Square root of mean difference
    
def CV(X):
    mean = sum(X)/float(len(X))
    try:
        return stdDev(X)/mean
    except ZeroDivisionError:
        return float('nan')
        
def makePlot(xVals, yVals, title, xLabel, yLabel, style,
             logX = False, logY = False):
    """Plots xVals vs. yVals with supplied titles and labels."""
    pylab.figure()
    pylab.title(title)
    pylab.xlabel(xLabel)
    pylab.ylabel(yLabel)
    pylab.plot(xVals, yVals, style)
    if logX:
        pylab.semilogx()
    if logY:
        pylab.semilogy()
        
def runTrial(numFlips):
    numHeads = 0
    for n in range(numFlips):
        if random.random() < 0.5:
            numHeads += 1
    numTails = numFlips - numHeads
    return (numHeads, numTails)
    
def flipPlot1(minExp, maxExp, numTrials):
    """Assumes minExp and maxExp positive ints; minExp < maxExp
        numTrials a positive integer
       Plots summaries of results of numTrials trials of
        2**minExp to 2**maxExp coin flips"""
    ratiosMeans, diffsMeans, ratiosSDs, diffsSDs = [], [], [], []
    ratiosCVs, diffsCVs = [], []
    xAxis = []
    for exp in range(minExp, maxExp + 1):
        xAxis.append(2**exp)
    for numFlips in xAxis:
        ratios = []
        diffs = []
        for t in range(numTrials):#for each x axis point, trial several times.
            numHeads, numTails = runTrial(numFlips)
            ratios.append(numHeads/float(numTails))
            diffs.append(abs(numHeads - numTails))
        ratiosMeans.append(sum(ratios)/float(numTrials))
        diffsMeans.append(sum(diffs)/float(numTrials))
        ratiosSDs.append(stdDev(ratios))
        diffsSDs.append(stdDev(diffs))
        ratiosCVs.append(CV(ratios))
        diffsCVs.append(CV(diffs))
    numTrialsString = ' (' + str(numTrials) + ' Trials)'
    title = 'Mean Heads/Tails Ratios' + numTrialsString
    makePlot(xAxis, ratiosMeans, title,
             'Number of flips', 'Mean Heads/Tails', 'bo', logX = True)
             
    title = 'SD Heads/Tails Ratios' + numTrialsString
    makePlot(xAxis, ratiosSDs, title,
             'Number of Flips', 'Standard Deviation', 'bo',
             logX = True, logY = True)
             
    title = 'Coeff. of Var. Heads/Tails Ratio' + numTrialsString
    makePlot(xAxis, ratiosCVs, title, 'Number of Flips',
             'Coeff. of Var.', 'bo', logX = True, logY = True)
             
    title = 'Mean abs(#Heads - #Tails)' + numTrialsString
    makePlot(xAxis, diffsMeans, title,
             'Number of Flips', 'Mean abs(#Heads - #Tails)', 'bo',
             logX = True, logY = True)
             
    title = 'SD abs(#Heads - #Tails)' + numTrialsString
    makePlot(xAxis, diffsSDs, title,
             'Number of Flips', 'Standard Deviation', 'bo',
             logX = True, logY = True)
             
    title = 'Coeff. of Var. abs(#Heads - #Tails)' + numTrialsString
    makePlot(xAxis, diffsCVs, title, 'Number of Flips',
             'Coeff. of Var.', 'bo', logX = True)
             
flipPlot1(4, 20, 20)
pylab.show()