Last updated on 2017/2560 3 12, a full moon day;     distribute i.e. Distribution;     Approx. 25distributions are available to read;

   IFF (  DEE) i.e. 10 dimensional patterns (also see: Network Topology) for this DOMAIN 's imaginary hyper space ... e.g. 2,3 dimensional imaginary hyper space teleportation, 3,4 dimensional imaginary hyper space teleportation, imaginary space crafts, imaginary space engineering and developments, ... in our Shakya universes ... ;    WHEN random number (s) is / are needed, random variable (s) must be calculated, and then WHAT random variable x will be defined into WHICH parameter of pressure machine ... ;

Develop, design, and engineer a new 2,3 dimensional differentiable manifold by 2,3 dimensional distribution formula [ for avoiding groups of stones "stars" in ACT2 space public traveling ... ];

_ WHICH 2, WHEN SYNC, NOT triangulate;

_ WHICH 3, WHEN SYNC AND triangulate;

  

ACT3 DNA growth pattern distribution: time + number = distance, WHERE time must be parallel time, and number must be based on natural time, ... ; Therefore, ɟ(x) = ... ; Also see: Plantation on the MOON;

  

Bernoulli distribution a.k.a. BE(p): ɟ(x) = { p IFF x = 1, (1 - p) IFF (x = 0), , , , ... ; THIS generates µ within ц (0, 1); RETURN 1 IFF (µ <= p), 0 IFF ELSE;

  

Beta distribution a.k.a. B(α, β): ɟ(x) = { (Γ(α + β)) / ((Γ(α)) (Γ(β))) ((x(α - 1)) (1 - x)β- 1) IFF (α > 0) AND (β > 0) AND (0 <= x <= 1), , , , , ... ; α = Integer((α))) AND β = Integer((β))); THIS generates y1 from Ģ(α, 1) AND y2 from Ģ(β, 1); x = (y1 / (y1 + y2)); RETURN x;

  

Binomial distribution a.k.a. BN(n, p): Probability mass function f with random variable x can be calculated as ɟ(x) = { (( n! ) / ((n - x)! x!))  ((px (1 - p))n-x) IFF (x = 0, 1, 2, ... , n-1, n), , , , , ... ; WHILE (n = Integer((n))) AND (0 < p < 1); THIS generates y1, y2, y3, ... , yn-1, yn from BE(p); RETURN y1 + y2 + y3 + ... + yn-1 + yn ;

  

Cauchy distribution a.k.a. C(α, β): ɟ(x) = { β / (π2 + ((x - α)2 ))) IFF (α > 0) AND  (β > 0) AND (-¥  < x < ¥), , , , , ... ; THIS generates µ within ц (0, 1); Probability density function's x is assigned as x = α - (β / tan (π µ)); RETURN x;

  

Chi-Square distribution a.k.a. X2(k): IFF (z1, z2, z3, ... , zk within N(0, 1)); y = i = 1Sk zi2; k is degrees of freedom; ɟ(x) = { ((x(( k / 2) - 1) exp (- x / 2)) / (Γ (k / 2) 2(k / 2))) IFF (x >= 0), , , , , ... ; Mean and variance are k, 2k; THIS generates zi; i = 1, 2, 3, ... , k, within N(0, 1); RETURN (z12 + z22 + z32 + ... + zk2);

distributing something, i.e. allocation;

 

D O M , document object model ;    
D C O M , distribute d component object model
;                  

  

Empirical distribution: ɟ(x) = { 0 IFF x < a1, (((i - 1) / (n - 1)) + (x - ai) / ((n - 1) (ai + 1 - ai))) IFF ((ai <= x <= ai+1) AND (1 <= i <= n - 1)), 1 IFF an <= x, , , ... ; THIS generates µ within ц (0, 1); RETURN ai + (((n -1) µ - i + 1) (ai+1 - ai)); WHILE i = Integer(((n - 1) µ + 1));

  

Erlang distribution: ... ;

  

Exponential distribution a.k.a. EXP(β): ɟ(x) = { (1 / β) e-(x / β) IFF ((0 <= x < ¥ ) AND (β > 0)), 0 IFF ELSE, , , , ... ; THIS generates u within ц (0, 1); RETURN -(β (ln (u)));

  

F distribution: ... ;

  

Gamma distribution a.k.a. Ģ(α, β): ɟ(x) = { ((xα - 1 e-(x / β) ) / βα Γ(α)) IFF (0 <= x < ¥ ) AND (α > 0) AND (β > 0)), 0 IFF ELSE, , , , ... ; Ģ(α, β) WHICH (((α β) = NOT constant) AND ((α β2) = NOT constant)); Ģ(1, β) = exp (β); WHILE α = Integer(()); THIS generates x = 0; REPEAT v within (EXP(1)); x= x + v; α= α - (1 = ((1))); UNTIL (α = 1); RETURN (β x);

  

Geometric distribution: ... ;

  

Logistic distribution: ... ;

  

Lognormal distribution a.k.a. LOGN(µ, s2): WHILE (x is from N(µ, s2) AND y = exp (x)), probability density function f(y) = { (1 / (√(2 π s y))) exp (- ((((ln y) - µ)2 ) / (2 s2))) IFF (0 <= y < ¥ ), 0 IFF ELSE, , , , ... ; Mean and variance are exp (µ + (s2 / 2)), ((exp(s2 )) - 1) exp (2µ + s2); THIS generates z within N(0, 1); x= (u + (s z)); RETURN exp(x);

(math) logistic distribution ... ;

  

Multi-normal distribution: ... ;

  

Negative Binomial distribution: ... ;

  

Normal distribution: ... ;

  

PDF, Probability Distribution Function: IFF Time . Space (Distance ab) PDF = (1/(b-a)) ... , WHERE Time is on X dimension, and PDF is on Y dimension;

i.e.

PDF=(1/(b-a)) ... ; Also see: 2011 August, Pg. 57, Computer, IEEE, www.computer.org;

  

Poisson distribution a.k.a. P(λ): ɟ(x) = { ((λx) e) / x! IFF (x = 0, 1, 2, ... ), 0 IFF ELSE, , , , ... ;         Mean is λ (λ > 0); x = 0; b = 1; Brunch: THIS generates u within ц (0, 1); b = b u; IF b >= e, then (x = x + 1) AND GOTO the Brunch; Return x;

  

Student's t distribution: ... ;

this DOMAIN, IFF location is our earth, Gene Therapy System ( Distribution (Iron) via blood proteins, bone marrow, enzymes, ferritin, hemoglobin, muscle, plasma transportation, tissue ), also see: Chemical Elements (Fe);

IFF location is one of the human beings livable moons, Body Length Index (BLI) auto adjustment, accordance with yellowish variations, SPL, diff shadow color, ... ;

Triangular distribution: ... ;

  

Uniform distribution: ... ;

  

Weibull distribution: ... ;

z-distribution standard normal distribution;

                   
standard normal distribution z - distribution ;    
  weight ;            

(z) distribution (-Z, +Z) Also see: heat sensing pattern ... ; thermal imaging pattern;

IFF (minus Z) is light depth, (plus Z) is hologram;
IFF
(minus Z) is hologram, (plus Z) is light depth;

In common, NOT (hot/ground reverse; hot/neutral reverse) 1st, WHICH means correct GFCI method alike; plus is positive potential, and so many AI designs have been without using minus (i.e. negative potential) for letting electrons flow (e.g. potential diff among short circuits) 2nd, also see: open ground; HOW cleverly letting the electrons flow WHERE controlling (-Z, +Z) is 3rd, do it yourself, also see: Monbusho level knowledge enhancement;      directional gravity;       i.e. our solar system might be moving from green to blue, in 2,3 dimensional;

this DOMAIN AI SYSTEM ( Cloud) weight to do elevating ... ;

Also read: [Uncertain Programming; Baoding Liu; 1999]; Also see: Algorithm; Fuzzy Support Vector Machine, this DOMAIN 's imaginary dimensional hyperspace craft; Please notice that 6 parameters have been intentionally use ... ;   Also see: Distributive Law; Notice that integer has been adjusted [cast: i.e. x = cast (y)] by natural time; FP, Fuzzy Parameters have been used in each fuzzy set { ... ; Also see: Mutual Exclusion's Set{...}, Duo-binary OSI Draft's Set{...};

For ACT3 stage developers only: also read that number 3 behaves as semantic in JUN time, and then time to develop ACT3 stage developments ... ; For ACT3 and ACT2 stage space mathematicians only: develop differentiable manifold in lie-groups mathematically; To do so, 1st to understand, star in Kanji writing character "sun at top, 2 green lines, 3 aqua lines", and then 2nd to understand 2,3 dimensional vector, and then design and engineer 2,3 dimensional distribution formula mathematically, 3rd to prove differentiable manifold in lie-groups; For space engineers only: Calculate the shaded 2D region: and how to solve horizontal area at certain vertical height; Before understanding the distribution of energy, M Theory of strings must be understood;

For computer system analysts only: Calculate 2 parameters values of system time (s), and then reverse engineer WHICH distribution has been used WHILE synchronization occurs among servers in Intranet; i.e. / / idlist,123:4567, /list comma     randomly distributed time stamp in integer   :   randomly distributed time stamp in integer comma has been prompted between computer A and B in a grid with TTL, Time to live < 15 ms;

distribute ... ;

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