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11 Cards in this Set
- Front
- Back
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Normal
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f(x)=[1/(sigma*sqrt(2pi))]*e^[-.5((x-mu)/sigma)^2]
Ex. Sample of averages (X bar) |
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Uniform
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f(x)= 0 if x<-a; 1/2a if -a<x<a; 1 if x>a
Ex. Variation limits are known and probability is constant |
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Exponential
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f(x)=lambda*e^(-lambda *x), x>0
Note: Reciprocal follows Poisson distribution. Ex. Model mean time between occurences (MTBR) |
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Lognormal
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f(x)=[1/(x*sigma*sqrt(2pi))]*e^[-.5((lnx-mu)/sigma)^2]
Note: If data is lognormal, transforming by taking logarithm yields normal distribution. Lognormal distribution is skewed right. |
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Weibull
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f(x)=[beta/theta]*[(x-delta)/theta]^(beta-1)*[ exp-((x-delta)/theta))^beta]
Ex. Used to model time to fail, time to repair, and material strength. If shape factor (beta)=1, Weibull is exponential. If shape factor is between 3 and 4, Weibull approximates normal. |
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Chi-Square
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f(x)=[(x^(nu/2-1))*e^-x/2]/[(2^nu/2)*Gamma(nu/2)], x>0
Ex. Statistical inference, formed by summing squares of standard normal random variables |
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F
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f(x)=[X/nu1]/[Y/nu2) if X and Y are chi-square random variables
Ex. ANOVA |
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Student's t
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f(x)=[[tau(nu+1)/2]/[tau*nu/2*sqrt(pi* nu)]]*(1+x^2/nu)^(-(nu+1)/2)
Ex. Used when sample size is small and standard deviation is unknown to compute confidence intervals |
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Binomial
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P(r)=[n!/(r!*(n-r)!)]*p^r*(1-p)^n-r
Ex. Sampling with replacement, approximation of hypergeometric. Approximated by normal when np>=5. |
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Poisson
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P(r)=[mu^r*e^-mu]/r!
Ex. Approximation of binomial when sample size is large and p is small (less than 0.1). |
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Hypergeometric
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P(r)=[C(d,r)*C(N-d, n-r)]/C[N,n]
Ex. Sampling without replacement; when population is small compared to sample size. |
