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71 Cards in this Set
- Front
- Back
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Cov[X, Y ]= |
E[(X − µX)(Y − µY )] E[XY ] − E[X]E[Y] |
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coefficient of variation |
σ/µ |
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correlation coefficient |
ρXY =Cov[X, Y ] / σXσY. |
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skewness
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µ^3σ^3=E[(X − µ)^3]/σ^3 |
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hazard rate function |
h(x) = f(x)/S(x) = −d/dx (ln S(x)). |
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Kurtosis |
=µ^4/σ^4=E[(X − µ)4]/σ^4 . |
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Where n-k+1= the number of trials in TvaR and s^2 is the sample variance of Tvar |
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Severity |
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Severity |
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Must have at least 5 if grouping |
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What distribution is given from a Beta where (a=b=1). |
Uniform with a lower bound of 0 and an upper bound of theta. |
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Where Fn(x) consist of Fn(x) the time period before and the current time period. |
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Likelihood Ratio Test |
The # DoF for the likelihood ratio test is the number of free parameters in the alternative modelminus the number of free parameters in the base model (null hypothesis). |
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Where b is the width. |
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Partial Credibility |
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Where r is the # of groups and n is the # of years. |
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Where r is the # of groups and n is the # of years. |
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For incomplete data, with censoring or truncation. |
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For complete data, without censoring or truncation. |
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Where n is the number observed and nf is the number needed for full credibility. |
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Variance of the posterior distribution. (Using Buhlmann approach) |
Var=(1-z)*a |
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Variance of the predictive distribution. (Using Buhlmann approach). |
Var=(1-z)*a+v |
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And Y is the observed value of the sorted data. |
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General Formula |
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General Formula |
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