The Sultonov Regression Model (SRM) - claiming to be a mathematical model of the market. - page 42

 
orb:
Isn't density limited to 0 to 1?

Density is not.
 
orb:
Isn't density limited to 0 to 1?
Of course it is bounded by one, but here: P=1+tHammasp(t/t;n;1;0), where tHammasp(t/t;n;1;0) is the distribution density function, varying from 0 to 1. See formula (7) of the paper.
 
yosuf:

Yes, I must have overdone it with the zeros...

in any regression to see equi flying into the sky is a talent...the main thing is to believe...))
 
anonymous:

Density - no.
let's say goodbye!) ignoramus.
 
orb:
goodbye!) ignoramus.


f(x,mu,sigma)=exp(-((x-mu)^2)/(2*sigma^2))/(sigma*sqrt(2*pi)) - the density of the normal distribution.

You, professor, will find it surprising that f(0, 0, 0.01)=39.89

 
yosuf:
Of course it is bounded by one, but here: P=1+tHammasp(t/t;n;1;0), where tHammasp(t/t;n;1;0) is the distribution density function, varying from 0 to 1. See formula (7) of the paper.

Out of the occupation, the unit is bounded by the non-invariant integral of the density from -inf to x.
 
anonymous:


f(x,mu,sigma)=exp(-((x-mu)^2)/(2*sigma^2))/(sigma*sqrt(2*pi)) - is the density of the normal distribution.

You, professor, will find it surprising that f(0, 0, 0.01)=39.89

I will check, and in general you are wrong, because 0 is a discrete value, and you use a continuous normal distribution law, respectively, you need to introduce a generalized density, because the random variable is mixed X, with possible values of x, which takes one discrete value of 0, the other continuous values!

 
orb:

and in general you got it wrong, because 0 is a discrete value, and you are using a continuous normal distribution law,

f(x, 0, 0.01) > 1 for any x in the interval [-0.027152;0.027152].

accordingly we have to introduce a generalized density,

necessarily :D

since the random variable is mixed X, with possible values of x, which takes one discrete value 0, the rest continuous values!

Really? Is the set of integers not discrete? Is it OK that x can take any value from the set of integers (as a subset for R)?

 
anonymous:

f(x, 0, 0.01) > 1 for any x in the interval [-0.027152;0.027152].

Absolutely :D

Really? Isn't the set of integers discrete? Is it OK that x can take any values from the set of integers (as a subset for R)?

Do you agree with the statement that m=0 is the mathematical expectation, or rather its estimate?

is sigma=0.01 the root of the variance estimate?

can you, model such a series?)) so the estimates are not taken from your head.

 
orb:

Do you agree with the statement that m=0 is the mathematical expectation, or rather its estimate?

is sigma=0.01 the root of the variance estimate?

can you, model such a series?)) so the estimates are not taken from your head.


They are not estimates, but the exact parameters of the distribution - expectation and standard deviation, professor :D

Of course, I can model such a series. Although it is completely unnecessary here, because your heresy with Yusuf is refuted by the analysis of the theoretical distribution function alone.

> x <- rnorm(100, 0, 0.01)
> x
  [1]  1.619572 e-02  6.798108 e-05 -3.627928 e-03  5.241613 e-03  1.273511 e-02  1.575794 e-03  7.716432 e-03  2.047810 e-03
  [9]  7.551535 e-03  2.707827 e-03 -1.783785 e-02  4.513436 e-03 -4.031291 e-03 -1.058043 e-02  1.421831 e-04 -6.639672 e-03
 [17] -1.434773 e-02 -4.618057 e-03 -1.411381 e-02 -1.459423 e-02 -7.465568 e-03 -7.713061 e-03  3.016197 e-02 -4.193879 e-03
 [25]  8.984821 e-03  7.578804 e-03 -1.256003 e-02  1.374785 e-02  1.239761 e-03 -1.547361 e-02 -1.735638 e-02 -6.853623 e-03
 [33]  5.278165 e-03 -1.917603 e-03 -3.507008 e-03  3.709349 e-03 -2.094672 e-04 -2.224821 e-03 -3.501819 e-03 -3.312482 e-03
 [41]  9.050138 e-03 -1.517038 e-03 -2.481432 e-04  1.132736 e-03  2.664056 e-03  2.146325 e-03 -1.762083 e-02 -8.993990 e-03
 [49]  8.303284 e-03 -5.353900 e-03 -2.845936 e-02 -1.556778 e-02  6.326411 e-04 -1.982076 e-02 -2.460851 e-03 -9.028795 e-03
 [57]  1.233104 e-02 -6.179724 e-03  1.614575 e-02 -9.239795 e-03  1.350007 e-02 -7.019569 e-03  1.463546 e-02  9.611378 e-03
 [65]  1.403177 e-02 -2.875648 e-03 -3.541369 e-03  9.854737 e-03  2.134445 e-03  3.010908 e-03 -9.468081 e-03  5.583229 e-03
 [73] -4.736917 e-03 -2.052099 e-03 -1.371189 e-02 -1.530808 e-03  8.776596 e-03 -1.272746 e-02  9.583266 e-03 -1.944051 e-02
 [81] -2.341326 e-03  4.766029 e-03 -7.953369 e-03  1.773432 e-02  8.939169 e-03  8.789134 e-03 -5.713990 e-03  4.144645 e-03
 [89]  6.384486 e-03  8.868000 e-03 -1.181570 e-02  4.893533 e-03 -3.452248 e-03 -1.525700 e-03  2.135513 e-02  1.633766 e-02
 [97] -6.266012 e-03 -5.332083 e-03  2.446737 e-02 -1.470896 e-02
> mean(x)
[1] -0.0003638158
> sd(x)
[1] 0.01055043