scholarly journals Asymptotics of the sample coefficient of variation and the sample dispersion

2010 ◽  
Vol 140 (2) ◽  
pp. 358-368 ◽  
Author(s):  
H. Albrecher ◽  
Sophie A. Ladoucette ◽  
Jef L. Teugels
Keyword(s):  
Coefficient Of Variation ◽  
Sample Coefficient Of Variation ◽  
Sample Dispersion

scholarly journals Domains of attraction of the real random vector (X,X2) and applications

2009 ◽  
Vol 86 (100) ◽  
pp. 41-53
Author(s):  
Edward Omey ◽  
Gulck van
Keyword(s):  
Asymptotic Behaviour ◽  
Random Vector ◽  
Coefficient Of Variation ◽  
Domain Of Attraction ◽  
Stable Law ◽  
Domains Of Attraction ◽  
Full Discussion ◽  
Definition Of ◽  
Sample Coefficient Of Variation ◽  
Sample Dispersion

Many statistics are based on functions of sample moments. Important examples are the sample variance s2(n), the sample coefficient of variation SV (n), the sample dispersion SD(n) and the non-central t-statistic t(n). The definition of these quantities makes clear that the vector defined by (?ni=1Xi, ?ni=1Xi2)plays an important role. In the paper we obtain conditions under which the vector (X,X2) belongs to a bivariate domain of attraction of a stable law. Applying simple transformations then leads to a full discussion of the asymptotic behaviour of SV(n) and t(n).

scholarly journals Limit distributions for the ratio of the random sum of squares to the square of the random sum with applications to risk measures

2006 ◽  
Vol 80 (94) ◽  
pp. 219-240 ◽  
Author(s):  
Sophie Ladoucette ◽  
Jef Teugels
Keyword(s):  
Coefficient Of Variation ◽  
Counting Process ◽  
Risk Measures ◽  
Asymptotic Properties ◽  
Random Variables ◽  
Random Sum ◽  
Convergence Conditions ◽  
Sample Coefficient Of Variation ◽  
Sample Dispersion ◽  
Erratic Behavior

Let {X1,X2, . . .} be a sequence of independent and identically distributed positive random variables of Pareto-type and let {N(t); t >_ 0} be a counting process independent of the Xi?s. For any fixed t> _ 0, define: TN(t) := X2 1 + X2 2 + ? ? ? + X2N (t) (X1 + X2 + ? ? ? + XN(t))2 if N(t) >_ 1 and TN(t) := 0 otherwise. We derive limits in distribution for TN(t) under some convergence conditions on the counting process. This is even achieved when both the numerator and the denominator defining TN(t) exhibit an erratic behavior (EX1 = ?) or when only the numerator has an erratic behavior (EX1 < ? and EX2 1 = ?). Armed with these results, we obtain asymptotic properties of two popular risk measures, namely the sample coefficient of variation and the sample dispersion. References.

On the percentage points of the sample coefficient of variation

Biometrika ◽  
1968 ◽  
Vol 55 (3) ◽  
pp. 580-581 ◽  
Author(s):  
BORIS IGLEWICZ ◽  
RAYMOND H. MYERS ◽  
RICHARD B. HOWE
Keyword(s):  
Coefficient Of Variation ◽  
Percentage Points ◽  
Sample Coefficient Of Variation

FINITE-SAMPLE MOMENTS OF THE COEFFICIENT OF VARIATION

2009 ◽  
Vol 25 (1) ◽  
pp. 291-297 ◽  
Author(s):  
Yong Bao
Keyword(s):  
Coefficient Of Variation ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
General Distribution ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Finite Sample Bias ◽  
Sample Coefficient Of Variation

We study the finite-sample bias and mean squared error, when properly defined, of the sample coefficient of variation under a general distribution. We employ a Nagar-type expansion and use moments of quadratic forms to derive the results. We find that the approximate bias depends on not only the skewness but also the kurtosis of the distribution, whereas the approximate mean squared error depends on the cumulants up to order 6.

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