t distribution with large degrees of freedom is the same as Normal (Gaussian) distribution with mean 0 and standard devitation 1 approximately.
  • normal[x_] := PDF[NormalDistribution[0, 1], x]
  • t[x_, nu_] := PDF[StudentTDistribution[nu]], x]
  • Plot[{normal[x], t[x, 3], t[x, 6], t[x, 20]}, {x, -6, 6},  PlotStyle -> {Black, Gray, Blue, Red}]
사용자 삽입 이미지
  • Five real random numbers x0 from the Gaussian distribution (0,1):
사용자 삽입 이미지

  • Five real random numbers x1 from the Gaussian distribution (mu,sigma) :
사용자 삽입 이미지
  • There is the following relation : x1 = x0*sigma + mu
사용자 삽입 이미지

Therefore, from a real random number from t distribution random number generator with nu, I can get the random magnetic field strength B_t as following:
사용자 삽입 이미지
,where t_random is generated by gsl_ran_tdist function as

random t distribution


In the random_t_distribution function, I used a sort of random number generator in order to get a random seed. The original random number generator, which is based on /dev/random, is shown in Advanced Linux Programming Chapter 6. I modified it as following:

random seed generator function


Secure Programming Cookbook for C and C++ (11.3 Using the Standard Unix Randomness Infrastructure) is also useful reference book on the web.
신고

'old memories > physics' 카테고리의 다른 글

t distribution and GSL random number generator  (0) 2007.07.02
Confidence Interval and Prediction Interval  (0) 2007.06.20
PhD thesis  (1) 2006.11.30
Tolerance  (3) 2006.11.08
posted by citadel
Confidence Interval (CI)
describes the uncertainty in $\bar Y$ as an estimate of $\mu$, where $\bar Y$ is the sample mean and $\mu$ the population(true) mean
  • 95% CI means that the true mean value will be inside this interval with 95% probability
  • Suppose repeated samples of Y_i are taken of the same size and at the same fixed values of X as were used to determine the fitted line above. Then of all the 95% CIs constructed for the mean value of Y for a given value of X, $X_0$ say, 95% of these intervals will contain the true value of this mean value of Y at $X_0$
Prediction Interval (PI)
describes the uncertainty in $\bar x$ as an estimate of the next measurement value.
95% PI means that next measurement value will be in the interval with 95% probability


reference
  • http//webche.ent.ohiou.edu/che408/Confidence%20Intervals_notes.ppt
  • Applied regression analysis - Darper, norman Richard. page 29 ..


신고

'old memories > physics' 카테고리의 다른 글

t distribution and GSL random number generator  (0) 2007.07.02
Confidence Interval and Prediction Interval  (0) 2007.06.20
PhD thesis  (1) 2006.11.30
Tolerance  (3) 2006.11.08
posted by citadel

PhD thesis

old memories/physics 2006.11.30 02:02
Writing the PhD thesis is so time-consuming work. Yes, definitely, it is too hard work for me. It is significantly different from master thesis.  At that time, I had no idea about what I was writing and also it was written on Korean.
User inserted image

During a whole day, just sit and type something. However, the next day, the almost everything, which was done the day before, must be modified or be deleted.  Sometime, I find the misunderstanding of my old calculation, then go back there and do the same thing as before.

However, I realize one important thing this: To write something is to find out what I did not understand and to engrave the specific knowledges on my stupid memory.
신고

'old memories > physics' 카테고리의 다른 글

t distribution and GSL random number generator  (0) 2007.07.02
Confidence Interval and Prediction Interval  (0) 2007.06.20
PhD thesis  (1) 2006.11.30
Tolerance  (3) 2006.11.08
posted by citadel