Hypo Variance is used to analyze the College English Test score distribution against the major, class, gender and grade etc.

1. A n a l y s i s o f C E T- 4 / C E T- 6 f o r J i a n g s u
U n i v e r s i t y S u q i a n C o l l e g e w i t h
H y p o / H y p e r Va r i a n c e s
Anaiysis of Gauss Complex Spectrum of Laplace Moment in Mandelbrot Fractal
Extracurricular Analysts：He Songting, You Ruomeng, Zhu Ling, Ling Zimu
Group Activity Tutors：Ke Jiang, Shi Hongwei, Xu Chongcai,
Jun Steed Huang
Dr. Laplace 270th birthday

2. 1 B a c k g r o u n d I n t r o d u c t i o n
2 C o m p l e x M o m e n t M o d e l
3 A n a l y s i s o f E x a m i n a t i o n R e s u l t s
CONTENTS

3. Chapter
1B a c k g r o u n d I n t r o d u c t i o n

4. Background Introduction: Let me Talk a Few Figures
Laplace is a French analyst, probability theorist and physicist, and an academician of the French Academy of Sciences. In 1812, he
published an important book, Probability Analysis Theory, which summarizes the research of probability theory at that time and discusses
the application of probability in astronomy.
Gauss is a Jewish, famous German mathematician, physicist, astronomer, geodesy, and one of the founders of modern mathematics. Gauss
was considered one of the most important mathematicians in history. He studied the complex plane of integer and enjoyed the name of the
prince of mathematics.
Mandelbrot moved to Paris with his family at an early age. Mandbo has spent most of his life in the United States and has the triple
nationality of Poland, France and the United States. Mandbo studies a wide range from mathematical physics to financial mathematics, but
his greatest achievement is the creation of fractal dimension geometry.

5. N o r m S p a c e o f I n t e g e r D i m e n s i o n
The most commonly used norm is p-norm.
If
then
When p takes 1, 2, and infinity, the following are
the simplest cases:
1-norm：
2-norm：
infinity norm：
Where 2-norm is the distance in the common sense.

 ],,,[ 21 nxxxx 
 pp
n
pp
p
xxxx
1
21  
 
 n
n
n
xxxx
xxxx
xxxx
,,,max 21
2122
2
2
1
2
21
1








6. D e f i n e s t h e N o r m S p a c e f o r F r a c t a l D i m e n s i o n s
• Fractional Norm:
, 1, 1,p
x l p r  
2 2
1
1 1 11 21 2 2
1
2 2
1
1 1
2
sup : ,( 1)
inf : ,(0 1)
yn n
i ir
rn i ir y
rr
i
yn ni
i ir
y i i
r
x y x
x x
x y x

  


  
    
    
      
  
      
     
    
 

 

7. T h e n t h e P r o b a b i l i t y S p a c e F r a c t a l M o m e n t
o f S t e e d F r a c t a l D i m e n s i o n i s D e r i v e d
• Fractional center moment:
Given as a discrete random variable,
exist, define order k center moment as
where
 E














 


 i
i
ikik
k E
i
k
EEE )()1()(
0












0
)()1(
i
ikii
EE
i
k

1< k < 3
Gamma Function
(-0.5)! = 1.7725
0.5! = 0.8862
1.5! = 1.3293
2.5! = 3.3234

8. F a c t o r i a l o f a n y n u m b e r
Gamma function, as an extension of factorial, is a meromorphic function defined in the range of
complex numbers, which is usually written as:
(1)The gamma function on the real number field is defined as:
(2)The gamma function on the complex number is defined as:
among ,This definition can be extended to the gamma function of nonpositive integers
except on the complex plane in the whole complex field by using the analytic extension principle.
  

 dtetx tx 1
0
  dtetz tz 


 1
0
  0Re z

9. H y p o Va r i a n c e














 


 i
i
ikik
k E
i
k
EEE )()1()(
0

When k=1.5,we called it Subvariance or Hypo Steed Variance
When k=2.0,we called it Normal Variance or Laplace Gauss Variance
When k=2.5,we called it Hypervariance or Super Steed Variance

10. Z o u Q i n g ， o f t h e I O WA U n i v e r s i t y ，
w r o t e t h e L a n g l a n d s P r o g r a m .
If you want to know the original proof, you can refer to：Definition of
Complex Hurst and Fractional Analysis for Stock Market Fluctuation:
https://link.springer.com/book/10.1007/978-3-662-47200-2
In 1796, when Gauss was 19 years old, he discovered the ruler
drawing method of regular 17 sides, which solved the difficult
problem which has been outstanding for more than 2000 years since
Euclidean time. In the same year, the law of quadratic reciprocity
was published and proved. That is, the supreme program of the
mathematical kingdom: the embryonic form of the Langlands
program!

11. A C o a l M i n e A r t i c l e W r i t t e n b y a
G r a d u a t e a t t h e U n i v e r s i t y o f N e w Yo r k
https://www.researchgate.net/publication/309666155_Analysis_of_Risk_Management_for_the_Coal_Mine_Operations

12. D i r e c t o r W a n g ' s I n t e l l i g e n t Tr a f f i c

13. M o r e R e f e r e n c e s

14. 2C o m p l e x M o m e n t M o d e l
Chapter

15. R e a l M o m e n t C o n t i n u o u s M o d e l
Expect
The expectation of a random variable (or statistic, the same below) is defined as its first order
primitive moment:
In definitions such as variance, expectation is also called the "center" of random variables.
Obviously, the center distance of the first order of any random variable is 0.
Variance
The variance of a random variable is defined as its second order central moment:
Skewness
The skewness of a random variable is defined as its third-order central moment:
   dxxxfx  


       


 dxxfxxxVar
2
       


 dxxfxxxS
3

16. R e a l M o m e n t D i s c r e t e M o d e l
1. Deviation coefficient measured in units using standard deviation
The skewness coefficient is recorded as the SK, formula:
SK is a dimensionless quantity, the value is usually between-3-+3, the greater the absolute value,
the greater the degree of deviation, when the distribution is right skewness, SK > 0, so it is also
called positive skewness; when the distribution is left skewness, SK < 0, so it is also called
negative skewness, but unless it is packet frequency distribution data, the number in SK
formula has great randomness.
2. Skewness coefficients measured using third-order central moments
The skewness coefficient is measured by the third order center distance divided by the cubic
power of the standard deviation, denoted as α=m3/σ3, and the formula is:
It's called the third-order center distance.
The skewness coefficient can be applied to any data. The calculation methods of α and SK are
different, so the results calculated according to the same data are different.

0MX
SK


0M
 3
3
1
  xx
N
m i

17. R e a l M o m e n t D i s c r e t e M o d e l
The skewness coefficient is the skewness coefficient of X. the skewness coefficient is used to
describe the distribution shape characteristics of the normal distribution.
Measure the asymmetry of geographical data distribution, depict the bias centered on the average
value,g1< 0, indicating negative deviation, that is, the mean value is on the left side of the peak
value; g1> 0, indicating the positive deviation, that is, the mean value is on the right side of the
peak value; g1 ≤ 0, indicating the symmetric distribution.

18. C o r e C o d e : J u s t 1 l i n e !
10%
20%
40%
60%
释迦摩尼出生为何一手指
Fake ten
thousand volumes
of books
Send a word of
truth % F1=1.5, F2=2.0, F3=2.5

19. T h e A p p e a r a n c e o f S t e e d P l o t
The length of the line indicates the difference between the best student and the worst student,
and the angle of the line indicates the ratio of the above average students to the below average students.

20. 3
A n a l y s i s o f E x a m i n a t i o n R e s u l t s
Chapter

21. S t e e d P l o t o f D i f f e r e n t G r a d e s , D i f f e r e n t
M a j o r s a n d D i f f e r e n t C l a s s e s
This chart takes the 2017 Suqian College Communications 4th Year grades,
the higher the line, the higher the pass rate of this major.

22. H i s t o g r a m o f D i f f e r e n t C l a s s e s i n D i f f e r e n t
M a j o r s o f t h e S a m e G r a d e
This chart is based on the grade 4 scores of grade students in December 2017.
Using hist histogram, the distribution of scores is displayed directly in the chart.

23. S t e e d P l o t o f D i f f e r e n t G r a d e s , D i f f e r e n t
M a j o r s a n d D i f f e r e n t C l a s s e s
For the 4th Year score of in December 2017, which shows the pass rate from high to low.
The length of the line segment indicates the difference between good and bad, the
inclination angle indicates the ratio of good to bad student, and the color is major.

24. T h e R e l a t i o n s h i p B e t w e e n E n d L e n g t h a n d P a s s R a t e
(y3-y1)^2+(x3-x1)^(1/2) pass rate Pearson correlation coefficient
8373.519571 0.2857 0.578514487
11817.33426 0.5000
3345.399018 0.0909
7226.443216 0.8400
11012.80838 0.8889
T h e R e l a t i o n s h i p B e t w e e n t h e E n d P o i n t A n g l e a n d P a s s R a t e
arctan[(y3-y1)/(x3-x1) pass rate Pearson correlation coefficient
0.475103764 0.2857 0.697975891
0.79095773 0.5000
0.717830516 0.0909
0.81843096 0.8400
0.913471314 0.8889

25. T h e R e l a t i o n s h i p B e t w e e n t h e L e n g t h O r i g i n a n d P a s s R a t e
(x1^2+y1^2)^(1/2) pass rate Pearson correlation coefficient
161.8412051 0.2857 0.371787916
220.2736496 0.5000
91.90950665 0.0909
138.5517107 0.8400
168.935299 0.8889
T h e R e l a t i o n s h i p B e t w e e n t h e O r i g i n A n g l e a n d P a s s R a t e
arctan(y1/x1) pass rate Pearson correlation coefficient
-0.653583014 0.2857 -0.562956166
-0.782111307 0.5000
-0.775497223 0.0909
-0.79845752 0.8400
-0.8126318 0.8889

26. variance pass rate
Pearson correlation coefficient
1584.4000 0.2857 0.489802372
2254.0000 0.5000
765.3223 0.0909
1381.8000 0.8400
1864.7000 0.8889







n
i
i
n
i
i
n
i
ii
yyxx
yyxx
r
1
2
1
2
1
)()(
))((
The Pearson correlation coefficient formula is as follows:
P e a r s o n C o r r e l a t i o n C o e f f i c i e n t B e t w e e n V a r i a n c e a n d
P a s s R a t e

27. S P S S S o f t w a r e A t l a s o f I B M C o m p a n y
Profession SPSS Atla Class SPSS Atla

28. S P S S A t l a s
Grade SPSS Atla
Gender SPSS Atla

29. S P S S A t l a s
Aggregate Score SPSS Atlas
Obviously, it is
not completely
normal Gaussian
distribution, so
it is necessary to
analyze with
Steed Variances
in depth

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