# 'old memories/physics'에 해당되는 글 4건

## t distribution and GSL random number generator

old memories/physics 2007.07.02 22:57
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}]
• Five real random numbers x0 from the Gaussian distribution (0,1):

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

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:
,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.

#### 'old memories > physics' 카테고리의 다른 글

 t distribution and GSL random number generator  (0) 2007.07.02 2007.06.20 2006.11.30 2006.11.08

## Confidence Interval and Prediction Interval

old memories/physics 2007.06.20 06:35
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 ..

#### 'old memories > physics' 카테고리의 다른 글

 t distribution and GSL random number generator  (0) 2007.07.02 2007.06.20 2006.11.30 2006.11.08

## 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.

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.

#### 'old memories > physics' 카테고리의 다른 글

 t distribution and GSL random number generator  (0) 2007.07.02 2007.06.20 2006.11.30 2006.11.08