NORMALNA DISTRIBUCIJA

<<Statistics`ContinuousDistributions`

<<Graphics`Colors`

g[x_] := 1/(2π)^(1/2) ^(-x^2/2)

Plot[g[x], {x, -2, 2}, PlotStyle→Hue[.9]]

[Graphics:HTMLFiles/gauss_4.gif]

-Graphics -

gnorma[x_, mu_, sigma_] := 1/(sigma * (2π)^(1/2)) ^(-(x - mu)^2/(sigma * 2))

Plot[gnorma[x, 0, 1], {x, -2, 2}, PlotStyle→Hue[.9]]

[Graphics:HTMLFiles/gauss_8.gif]

-Graphics -

Plot[gnorma[x, 1, 1], {x, -2, 2}, PlotStyle→Hue[.9]]

[Graphics:HTMLFiles/gauss_11.gif]

-Graphics -

Plot[{gnorma[x, 0, 3], gnorma[x, 0, 1]}, {x, -4, 4}, PlotStyle→ {Hue[.2], Red}]

[Graphics:HTMLFiles/gauss_14.gif]

-Graphics -

Plot[{gnorma[x, 0, 3], gnorma[x, 0, 1/2], gnorma[x, 0, 1]}, {x, -2, 2}, PlotStyle→ {Hue[.2], Hue[.5], Red}]

[Graphics:HTMLFiles/gauss_17.gif]

-Graphics -

G[x_] := 1/(2π)^(1/2) ∫_ (-∞)^x^(-t^2/2) t

Plot[G[x], {x, -2, 2}, PlotStyle→Hue[.6]]

[Graphics:HTMLFiles/gauss_21.gif]

-Graphics -

NormalDistribution[μ, σ]

NormalDistribution[μ, σ]

n01 = NormalDistribution[0, 1]

NormalDistribution[0, 1]

cdfnormalna = CDF[n01, x]

1/2 (1 + Erf[x/2^(1/2)])

pdfnormalna = PDF[n01, x]

^(-x^2/2)/(2 π)^(1/2)

Plot[{cdfnormalna, pdfnormalna}, {x, -2, 2}, PlotStyle→ {Hue[.6], Red}]

[Graphics:HTMLFiles/gauss_32.gif]

-Graphics -

GAMA DISTRIBUCIJA

Table[Gamma[j], {j, 10}]

{1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880}

gdist = GammaDistribution[3, 1]

GammaDistribution[3, 1]

cdfgama = CDF[gdist, x]

GammaRegularized[3, 0, x]

pdfgama = PDF[gdist, x]

1/2 ^(-x) x^2

Plot[{cdfgama, pdfgama}, {x, 0, 5}, PlotStyle→ {Hue[.6], Red}]

[Graphics:HTMLFiles/gauss_41.gif]

-Graphics -

HI KVADRAT DISTRIBUCIJA

hidist = ChiDistribution[3]

ChiDistribution[3]

cdfhi = CDF[hidist, x]

GammaRegularized[3/2, 0, x^2/2]

pdfhi = PDF[hidist, x]

^(-x^2/2) 2/π^(1/2) x^2

Plot[{cdfhi, pdfhi}, {x, 0, 5}, PlotStyle→ {Hue[.6], Red}]

[Graphics:HTMLFiles/gauss_48.gif]

-Graphics -

STUDENTOVA DISTRIBUCIJA

stdist = StudentTDistribution[3]

StudentTDistribution[3]

cdfstudent = CDF[stdist, x]

1/2 (1 + BetaRegularized[3/(3 + x^2), 1, 3/2, 1/2] Sign[x])

pdfstudent = PDF[stdist, x]

(6 3^(1/2))/(π (3 + x^2)^2)

Plot[{cdfstudent, pdfstudent}, {x, -3, 3}, PlotStyle→ {Hue[.6], Red}]

[Graphics:HTMLFiles/gauss_55.gif]

-Graphics -

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