Last updated on
2017/2561
8
7,
a full moon day;
distribute i.e. ** Distribution**;
Approx. 25＋distributions 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 y_{1} from **Ģ(α, 1)**
AND y_{2}
from **Ģ(β, 1)**; x = (y_{1} / (y_{1}
+ y_{2})); 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!))
((p^{x} (1 - p))^{n-x}) IFF (x = 0, 1, 2, ... , n-1, n),
,
,
,
,
... ; WHILE (n = Integer((n)))
AND
(0 < p < 1);
THIS generates y_{1}, y_{2}, y_{3}, ... , y_{n-1},
y_{n} from **BE(p)**; RETURN y_{1}
+ y_{2 }+ y_{3 }+ ... + y_{n-1 }+ y_{n} ;

。

Cauchy distribution a.k.a. **
C(α, β)**:
ɟ(x) = { β / (π
(β^{2} + ((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. **X ^{2}(k)**:
IFF (z

。

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 < a_{1}, (((i - 1) / (n - 1)) + (x - a_{i})
/ ((n - 1) (a_{i + 1} - a_{i}))) IFF ((a_{i} <= x <= a_{i+1})
AND (1 <=
i <= n - 1)), 1 IFF a_{n} <= x,
,
,
... ;
THIS generates µ within ц (0, 1); RETURN a_{i} + (((n -1) µ - i +
1) (a_{i+1} - a_{i}));
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) =
{ ((x^{α - 1} e^{-(x / β)} ) / β^{α} Γ(α)) IFF (0
<= x < ¥ ) AND
(α > 0) AND
(β > 0)), 0 IFF ELSE,
,
,
,
... ; Ģ(α, β)
WHICH (((α β) = NOT
constant) AND
((α β^{2}) = 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, s**^{2}**)**:
WHILE (x is from N(µ, s^{2})
AND
y = exp (x)), probability density function f(y) = { (1 / (√(2
π
s y))) exp (- ((((ln y) - µ)^{2} ) / (2
s^{2}))) IFF (0 <= y <
¥ ), 0 IFF ELSE,
,
,
,
... ; Mean and variance are exp (µ + (s^{2}
/ 2)), ((exp(s^{2}
)) - 1) exp (2µ + s^{2});
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,
**P**robability **D**istribution
**F**unction: 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) = { ((λ^{x}) e^{-λ})
/ 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^{-λ}, 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, **F**uzzy **P**arameters 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 ... ;