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8: Distribuciones de fórmula, no paramétricas y derivadas
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Algoritmos de núcleo
Modele pagos de reclamos para seguros
Calcule la media de pago de reclamos hechos por una compañía de seguros usando una transformación por partes de la distribución de pérdidas.
In[1]:=
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LossCDF = ((1 - q) + q (1 - E^(-a x))) HeavisideTheta[ x]; Loss\[ScriptCapitalD] = ProbabilityDistribution[{"CDF", LossCDF}, {x, -\[Infinity], \[Infinity]}, Assumptions -> a > 0 && 0 < q < 1]; PayoutFunction[x_] := Piecewise[{{0, x <= d}, {x - d, d < x < s + d}, {s, x >= s + d}}]; g = Plot[PayoutFunction[x] /. {d -> 400, s -> 1000}, {x, 0, 1800}, PlotStyle -> {Thickness[0.01]}, Filling -> Axis, Exclusions -> None]; Payout\[ScriptCapitalD] = TransformedDistribution[PayoutFunction[x], x \[Distributed] Loss\[ScriptCapitalD], Assumptions -> d > 0 && s > 0 && 0 < q < 1 && a > 0]; m = Mean[Payout\[ScriptCapitalD]];
In[2]:=
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Framed[Show[g, ImageSize -> 500, PlotLabel -> Style[Grid[{{"Loss Probability = ", q}, {"Loss Distribution = ", ExponentialDistribution[a]}, {"Deductible = ", d}, {"Benefit Limit = ", s}, {"Mean Claim Payment = ", m}}, BaseStyle -> {FontFamily -> "Verdana"}, Alignment -> {{Right, Left}, Automatic}], FontSize -> 14, Bold]], RoundingRadius -> 10, FrameStyle -> GrayLevel@0.3, FrameMargins -> 10, ImageSize -> 550, Background -> Lighter[LightBrown, 0.3]]
Out[2]=