Table 1 Statistical Terms and Definitions 

 It should be noted that in the present work only estimates of the statistical parameters can be 



given 

 variate 



Property under study, for example, magnitude of stress variation, height of 

 waves. 



N 



2 a,^ 



The mean square value of a;, E = ' — - 



P{Xa) 



p(x) 

 population 



sample 

 c.d.f. 



d.f. 



Probability of the event x ■^ Xa with respect to the random experiment e. The 

 probability P means that in a long series of repetitions of c it is practically 

 certain that the relative frequency of occurrence of a; < JTa is equal to P where 

 < P < I. A value of P = 1 indicates that the event will occur with every 

 experiment «, P = indicates that the event will never occur. 



= f P(x) 

 ax 



Aggregate of all the members of the distribution subject to a statistical 

 study. The members may be individual measurements or the results of indi- 

 vidual experiments. 



Number of N members drawn (usually at random) from the population. Here 

 N is the "sample size." 



Abbreviation of the term "cumulative distribution function" P(x) which 

 denotes the probability that the variate x will take on a value less than or 

 equal to a;, i.e., P (x^) - P[x -^x^]. 



Abbreviation of the term "distribution function" p(x) which is the derivative 

 of P(ar) with respect to x, i.e.. 



p (a;) = -2- P (a;) and 

 dx 





p(x) dx = \ 



eV^ 



mean value of x 



variance of x 



standard deviation 

 quantile or fractile 



confidence bands 

 random 



N 

 1 X. 



= -i^ii — where x- is the individual member of the population or sample and N 

 is the number of members of the population or sample. 

 Mean value of a sample of values of x 

 Mean value of the population. 



I (x, 



■xf 



N - 1 



The variance is a measure of the dispersion of the values of 



x. The greater the variance the greater the dispersion. 



Variance of the population. 



Square root of the variance 



Corresponding to a given value of the c.d.f. P{x), there is a value of the 

 variate below which a fraction P{x) of all the members of the population lie. 

 The value of this variate is the quantile or fractile corresponding to P(x). 



Interval within which the "true" distribution will fall with a certain probability. 



A method of drawing a sample when each member of the population has an equal 

 chance of selection. 



