Exemple #1
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def sampling_distribution():
    fig, ax = plt.subplots(1, 1)
    #display the probability density function
    df = 10
    x=np.linspace(t.ppf(0.01, df), t.ppf(0.99, df), 100)
    ax.plot(x, t.pdf(x, df))
    
    #simulate the sampling distribution
    y = []
    for i in range(1000):
        r = norm.rvs(loc=5, scale=2, size=df+1)
        rt =(np.mean(r)-5)/np.sqrt(np.var(r)/df)
        y.append(rt)

    ax.hist(y, normed=True, alpha=0.2)
    plt.savefig('sampling_distribution.png')
Exemple #2
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def t_distribution():
    fig, ax = plt.subplots(1, 1)
    #display the probability density function
    df = 10
    x=np.linspace(-4, 4, 100)
    ax.plot(x, t.pdf(x,df))
    
    #simulate the t-distribution
    y = []
    for i in range(1000):
        rx = norm.rvs()
        ry = chi2.rvs(df)
        rt = rx/np.sqrt(ry/df)
        y.append(rt)

    ax.hist(y, normed=True, alpha=0.2)
    plt.savefig('t_distribution.png')
Exemple #3
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def sampling_distribution():
    fig, ax = plt.subplots(1, 1)
    #display the probability density function
    dfn, dfm = 10, 5
    x=np.linspace(f.ppf(0.01, dfn, dfm), f.ppf(0.99, dfn, dfm), 100)
    ax.plot(x, f.pdf(x, dfn, dfm))
    
    #simulate the sampling distribution
    y = []
    for i in range(1000):
        r1 = norm.rvs(loc=5, scale=2, size=dfn+1)
        r2 = norm.rvs(loc=3, scale=2, size=dfm+1)
        rf =np.var(r1)/np.var(r2)
        y.append(rf)

    ax.hist(y, normed=True, alpha=0.2)
    plt.savefig('sampling_distribution.png')
Exemple #4
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def sampling_distribution():
    fig, ax = plt.subplots(1, 1)
    #display the probability density function
    x = np.linspace(-4, 4, 100)
    ax.plot(x, norm.pdf(x))

    #simulate the sampling distribution
    y = []
    n=100
    for i in range(1000):
        r = expon.rvs(scale=1, size=n)
        rsum=np.sum(r)
        z=(rsum-n)/np.sqrt(n)
        y.append(z)

    ax.hist(y, normed=True, alpha=0.2)
    plt.savefig('sampling_distribution.png')
Exemple #5
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def F_distribution():
    fig, ax = plt.subplots(1, 1)
    #display the probability density function
    dfn, dfm = 10, 5
    x = np.linspace(f.ppf(0.01, dfn, dfm), f.ppf(0.99, dfn, dfm), 100)
    ax.plot(x, f.pdf(x, dfn, dfm))
    
    #simulate the F-distribution
    y = []
    for i in range(1000):
        rx = chi2.rvs(dfn)
        ry = chi2.rvs(dfm)
        rf = np.sqrt(rx/dfn)/np.sqrt(ry/dfm)
        y.append(rf)

    ax.hist(y, normed=True, alpha=0.2)
    plt.savefig('F_distribution.png')
Exemple #6
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def chi2_distribution():
    fig, ax = plt.subplots(1, 1)
    #display the probability density function
    df = 10
    x=np.linspace(chi2.ppf(0.01, df), chi2.ppf(0.99, df), 100)
    ax.plot(x, chi2.pdf(x,df))
    
    #simulate the chi2 distribution
    y = []
    n=10
    for i in range(1000):
        chi2r=0.0
        r = norm.rvs(size=n)
        for j in range(n):
            chi2r=chi2r+r[j]**2
        y.append(chi2r)

    ax.hist(y, normed=True, alpha=0.2) 
    plt.savefig('chi2_distribution.png')