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Stock market 1987 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Black Monday October 19, 1987 Dropped 508 points 1,738.

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Presentation on theme: "Stock market 1987 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Black Monday October 19, 1987 Dropped 508 points 1,738."— Presentation transcript:

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3 Stock market 1987 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Average: 2562 1 SD – 68 % : 2468.8 – 2655.2 2 SD – 95 % : 2375.6 – 2748.4 3 SD – 99.7 % : 2282.4 – 2841.6 Average: 2562 1 SD – 68 % : 2468.8 – 2655.2 2 SD – 95 % : 2375.6 – 2748.4 3 SD – 99.7 % : 2282.4 – 2841.6

4 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Standard Deviation%Frequency Approx. frequency for daily event ± 1σ 68.268,949,213,708,6 1 in 3 Twice a week ± 1.5σ 86.638,559,746,228,4 1 in 7 Weekly ± 2σ 95.449,973,610,364,2 1 in 22 Every three weeks ± 2.5σ 98.758,066,934,844,8 1 in 81 Quarterly ± 3σ 99.730,020,393,674,0 1 in 370 Yearly ± 3.5σ 99.953,474,184,192,9 1 in 2,149 Every six years ± 4σ 99.993,665,751,633,4 1 in 15,787 Every 43 years (twice in a lifetime) ± 4.5σ 99.999,320,465,375,1 1 in 147,160 Every 403 years ± 5σ 99.999,942,669,685,6 1 in 174,427,8 Every 4,776 years (once in recorded history) ± 5.5σ 99.999,996,202,087,5 1 in 263,302,54 Every 72,090 years ± 6σ 99.999,999,802,682,5 1 in 506,797,346 Every 1.38 million years (history of humankind) ± 6.5σ 99.999,999,991,968,0 1 in 124,501,973,93 Every 34 million years ± 7σ 99.999,999,999,744,0 1 in 390,682,215,445 Every 1.07 billion years Standard Deviation%Frequency Approx. frequency for daily event ± 1σ 68.268,949,213,708,6 1 in 3 Twice a week ± 1.5σ 86.638,559,746,228,4 1 in 7 Weekly ± 2σ 95.449,973,610,364,2 1 in 22 Every three weeks ± 2.5σ 98.758,066,934,844,8 1 in 81 Quarterly ± 3σ 99.730,020,393,674,0 1 in 370 Yearly ± 3.5σ 99.953,474,184,192,9 1 in 2,149 Every six years ± 4σ 99.993,665,751,633,4 1 in 15,787 Every 43 years (twice in a lifetime) ± 4.5σ 99.999,320,465,375,1 1 in 147,160 Every 403 years ± 5σ 99.999,942,669,685,6 1 in 174,427,8 Every 4,776 years (once in recorded history) ± 5.5σ 99.999,996,202,087,5 1 in 263,302,54 Every 72,090 years ± 6σ 99.999,999,802,682,5 1 in 506,797,346 Every 1.38 million years (history of humankind) ± 6.5σ 99.999,999,991,968,0 1 in 124,501,973,93 Every 34 million years ± 7σ 99.999,999,999,744,0 1 in 390,682,215,445 Every 1.07 billion years Standard Deviation%Frequency Approx. frequency for daily event ± 1σ 68.268,949,213,708,6 1 in 3 Twice a week ± 1.5σ 86.638,559,746,228,4 1 in 7 Weekly ± 2σ 95.449,973,610,364,2 1 in 22 Every three weeks ± 2.5σ 98.758,066,934,844,8 1 in 81 Quarterly ± 3σ 99.730,020,393,674,0 1 in 370 Yearly ± 3.5σ 99.953,474,184,192,9 1 in 2,149 Every six years ± 4σ 99.993,665,751,633,4 1 in 15,787 Every 43 years (twice in a lifetime) ± 4.5σ 99.999,320,465,375,1 1 in 147,160 Every 403 years ± 5σ 99.999,942,669,685,6 1 in 1,744,278 Every 4,776 years (once in recorded history) ± 5.5σ 99.999,996,202,087,5 1 in 26,330,254 Every 72,090 years ± 6σ 99.999,999,802,682,5 1 in 506,797,346 Every 1.38 million years (history of humankind) ± 6.5σ 99.999,999,991,968,0 1 in 12,450,197,393 Every 34 million years ± 7σ 99.999,999,999,744,0 1 in 390,682,215,445 Every 1.07 billion years Standard Deviation%Frequency Approx. frequency for daily event ± 1σ 68.268,949,213,708,6 1 in 3 Twice a week ± 1.5σ 86.638,559,746,228,4 1 in 7 Weekly ± 2σ 95.449,973,610,364,2 1 in 22 Every three weeks ± 2.5σ 98.758,066,934,844,8 1 in 81 Quarterly ± 3σ 99.730,020,393,674,0 1 in 370 Yearly ± 3.5σ 99.953,474,184,192,9 1 in 2,149 Every six years ± 4σ 99.993,665,751,633,4 1 in 15,787 Every 43 years (twice in a lifetime) ± 4.5σ 99.999,320,465,375,1 1 in 147,160 Every 403 years ± 5σ 99.999,942,669,685,6 1 in 1,744,278 Every 4,776 years (once in recorded history) ± 5.5σ 99.999,996,202,087,5 1 in 26,330,254 Every 72,090 years ± 6σ 99.999,999,802,682,5 1 in 506,797,346 Every 1.38 million years (history of humankind) ± 6.5σ 99.999,999,991,968,0 1 in 12,450,197,393 Every 34 million years ± 7σ 99.999,999,999,744,0 1 in 390,682,215,445 Every 1.07 billion years Is there life after 3 Standard Deviations…?

5 Stock market 1987 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Average: 2562 1 SD – 98 % : 2468.8 – 2655.2 2 SD – 95 % : 2375.6 – 2748.4 3 SD – 99.7 % : 2282.4 – 2841.6 Average: 2562 1 SD – 98 % : 2468.8 – 2655.2 2 SD – 95 % : 2375.6 – 2748.4 3 SD – 99.7 % : 2282.4 – 2841.6

6 Los Angeles Earthquakes Northridge Earthquake January 17, 1994 Magnitude 6.7 Property damage: > 20 billions Oct. 17, 1988 Loma Prieta, CA (San Francisco Bay Area) Mag.: 6.9 Oct. 17, 1988 Loma Prieta, CA (San Francisco Bay Area) Mag.: 6.9 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD

7 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Scale X-axis mSec 0 – 6 Phone Traffic - Internet Traffic

8 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Scale X-axis mSec 0 – 6 0 – 60 Phone Traffic - Internet Traffic

9 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Scale X-axis mSec 0 – 6 0 – 60 0 – 600 (0.6 sec) Phone Traffic - Internet Traffic

10 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Scale X-axis mSec 0 – 6 0 – 60 0 – 600 (0.6 sec) 0 – 3000 ( 3 sec.) Phone Traffic - Internet Traffic Scale Y-axis 60 – 160 600 – 1,600 6,000 – 14,000 40,000 – 80,000

11 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD 36 37 38 38 39 39 40 40 40 40 41 41 41 41 41 41 42 42 42 42 42 42 42 43 43 43 43 43 43 43 43 44 44 44 44 44 44 44 44 44 45 45 45 45 45 45 45 45 45 45 46 46 46 46 46 46 46 46 46 46 47 47 47 47 47 47 47 47 47 48 48 48 48 48 48 48 48 49 49 49 49 49 49 49 50 50 50 50 50 50 51 51 51 51 52 52 53 53 54 55 361 371 382 392 404 416 427 438 449 4510 4610 479 488 497 506 514 522 532 541 551 Power Law Distribution Power Law Distribution Normally Distributed Bell Shape Distributions Normally Distributed Bell Shape Distributions n = 100 3622 3712 389 397 406 415 425 434 444 453 463 473 483 492 502 512 522 532 542 552 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 37 37 37 37 37 37 37 37 37 37 37 37 38 38 38 38 38 38 38 38 38 39 39 39 39 39 39 39 40 40 40 40 40 40 41 41 41 41 41 42 42 42 42 42 43 43 43 43 44 44 44 44 45 45 45 46 46 46 47 47 47 48 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55

12 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD

13 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Power Law Non Bell Shape Distribution Fractal Power Power Law Non Bell Shape Distribution Fractal Power Normally Distributed Bell Shape Distributions Normally Distributed Bell Shape Distributions People heights Body Temperatures Length of fingers Phone networks traffic People heights Body Temperatures Length of fingers Phone networks traffic People incomes Earthquake intensities Stock market values Internet networks traffic People incomes Earthquake intensities Stock market values Internet networks traffic Probability Mean – Median - Mode Standard Deviations Regression Analysis Probability Mean – Median - Mode Standard Deviations Regression Analysis Power Dimensions Slope in log – log plots Grid counting Power Dimensions Slope in log – log plots Grid counting

14 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD

15 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD D = 2.3 D = 2.8 D = 1.98 D = 3 D = 2 D = 1 Dimensions as we know it Dimensions you may not think about… Koch  Cesaro Cesaro   Solid  Solid

16 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD 1 1 = 1 2 1 = 2 3 1 = 3 1 2 = 1 2 2 = 4 3 2 = 9 1 3 = 1 2 3 = 8 3 3 = 27 log 3 0.477 ------- = --------- = 1 log 3 0.477 ------- = --------- = 1 log 3 0.477 Log 9 0.954 ------- = --------- = 2 log 3 0.477 Log 9 0.954 ------- = --------- = 2 log 3 0.477 Log 27 1.431 ------- = --------- = 3 log 3 0.477 Log 27 1.431 ------- = --------- = 3 log 3 0.477 log Small pieces log Divisions Power Dimension log Small pieces log Divisions Power Dimension divisions D = Sp (Small Pieces) div. D = Sp log(div. D ) = log(Sp) D x log(div.) = log(Sp) log(Sp) D = ------------ log(div.) log(Sp) D = ------------ log(div.)

17 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD 1.5561.332 1.5681.090 1.5800.949 1.5910.845 1.6020.763 1.6130.699 1.6230.653 1.6330.602 1.6430.556 1.6530.519 1.6630.491 1.6720.462 1.6810.431 1.6900.398 1.6990.380 1.7080.362 1.7160.342 1.7240.322 1.7320.301 1.7400.279 3622 3712 389 397 406 415 425 434 444 453 463 473 483 492 502 512 522 532 542 552 Values – Freq. Exponential Curve Linear-Linear Scales (1 – 2 – 3 – 4) Logarithmic Curve Log – Log Scales (1 – 10 – 100 – 1000) Slope [log X/log Y] Power Dimension Slope [log X/log Y] Power Dimension X log X - log Y Y X/Y = Slope log(Values) D = ----------------- ~ -0.33 log(Freq.) log(Values) D = ----------------- ~ -0.33 log(Freq.) X - Y Freq. = (Values) -D

18 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD

19 What does all this has to do with Randomness? Normally Distributed Bell Shape Distributions Normally Distributed Bell Shape Distributions 35 57 ∞ 0 Power Law Distribution Power Law Distribution Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD

20 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Phone Traffic - Internet Traffic Northridge Earthquake January 17, 1994 Magnitude 6.7 LOSS RATIO: 2,273 Property damage: > 20 billions Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50 Black Monday October 19, 1987 Dropped 508 points 1,738 20 SD (8.8) 1 x 10 -50

21 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Known Asteroids that travel near Earth Some Interesting Examples David Morrison, who has the delightful title "director of space" at the NASA Ames Research Center, likes to say that the number of people searching for threatening astronomical objects is 11 times smaller than the staff of one McDonald's restaurant." Time June 9, 2014

22 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Some Interesting Examples People’s heights Average 57 countries 5 ft 8 in. St.Dev.: 3 in. People’s heights Average 57 countries 5 ft 8 in. St.Dev.: 3 in. Chandra Bahadur Dangi of Nepal 1 ft 9 ½ in Chandra Bahadur Dangi of Nepal 1 ft 9 ½ in 16 Std. Dev. Robert Pershing Wadlow of USA 8 ft 11 in Robert Pershing Wadlow of USA 8 ft 11 in 13 Std. Dev. + 4 σ ….. 6 ft 8 in - 4 σ ….. 4 ft 7 in.

23 Randomness: Does Randomness Rule Our Lives? (SDGs/14b-RAN) ©Carlos Lemmi, PhD Muth distribution Normal distribution Weibull distribution Gamma distribution Gumbel distribution Uniform distribution Gompertz distribution Chi square distribution Power Law distribution Right-truncated normal Log normal distribution Log-logistic distribution Exponential distribution Half-normal distribution Exponential power distribution Ratio distribution of two uniform distributions Ratio distribution of two exponential distributions Ratio distribution of two half-normal distributions Ratio distribution of two right-truncated normal distributions Ratio distribution of two chi-square distributions (the F distribution) Muth distribution Normal distribution Weibull distribution Gamma distribution Gumbel distribution Uniform distribution Gompertz distribution Chi square distribution Power Law distribution Right-truncated normal Log normal distribution Log-logistic distribution Exponential distribution Half-normal distribution Exponential power distribution Ratio distribution of two uniform distributions Ratio distribution of two exponential distributions Ratio distribution of two half-normal distributions Ratio distribution of two right-truncated normal distributions Ratio distribution of two chi-square distributions (the F distribution) Other Distributions of data B-612 Nursery School Really… this is all you earthlings know? We learned these at the B-612 Nursery School… Really… this is all you earthlings know? We learned these at the B-612 Nursery School… Plato’s Allegory of the Cave

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