1 / 11

Probability Density Function (pdf) continuous distributions

Probability Density Function (pdf) continuous distributions. f(x) >= 0 all x f(x) is the “likelihood” of x integral under f(x) is exactly 1.0. Cumulative Distribution Function (cdf). F(x)=Pr(x<=X) probability X is <= x area under pdf from -inf up to x. FREQUENCY TABULATION .

kentaro
Télécharger la présentation

Probability Density Function (pdf) continuous distributions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Probability Density Function (pdf) continuous distributions • f(x) >= 0 all x • f(x) is the “likelihood” of x • integral under f(x) is exactly 1.0

  2. Cumulative Distribution Function (cdf) • F(x)=Pr(x<=X)probability X is <= x • area under pdf from -inf up to x

  3. FREQUENCY TABULATION • Interval Freq Rel Cum • Freq Prob • 40-44 22 .11 .11 • 44-48 46 .23 .34 • 48-52 74 .37 .71 • 52-56 52 .26 .97 • 56-60 6 .03 1.00

  4. HISTOGRAM DISTRIBUTION ~ FREQUENCY TABULATION

  5. CDF for HISTOGRAM DISTRIBUTION

  6. MEDIAN, 1st & 3rd QUARTILE from CDF for HISTOGRAM Q1 M Q3

  7. INTERPOLATION FORMULA for FRACTILE given cumulative probability xk = left end-point of interval xk+1 = right end-point of interval pk = cum prob at left end-point of interval pk+1 = cum prob at right end-point of interval p = given cum prob between pk and pk+1

  8. INTERPOLATION FORMULA for cumulative probability given x xk = left end-point of interval xk+1 = right end-point of interval pk = cum prob at left end-point of interval pk+1 = cum prob at right end-point of interval x = given variable value between xk and xk+1

  9. MEAN VALUE FORMULA for HISTOGRAM DISTRIBUTION • Interval Mid-points • mk = (xk + xk+1)/2 • Interval Probabilities • pk = Pk+1 - Pk • Mean Value • µ=Sum of pk * mk =

  10. VARIANCE FORMULA for HISTOGRAM DISTRIBUTION • AVERAGE of x2 for each interval • mi2 = (xi2 + xixi-1 + xi-12)/3 • SECOND MOMENT • Sum of pi mi2 • VARIANCE • σ2=Second Moment - (mean)^2 • STANDARD DEVIATION • sqrt(Variance)

  11. Example Computations • MEAN = .11*42 + .23*46 + .37*50 +.26*54 + .03*58 = 49.48 • SECOND MOMENT • VARIANCE

More Related