Difference between revisions of "Quantile"
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+ | |valign="top"|{{Ref|B}}|| L. Breiman, "Statistics" , Houghton Mifflin (1973) pp. 231ff {{MR|0359089}} {{ZBL|0289.62001}} | ||
+ | |- | ||
+ | |valign="top"|{{Ref|C}}|| H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946) pp. 181; 367 {{MR|0016588}} {{ZBL|0063.01014}} | ||
+ | |} |
Revision as of 08:57, 28 May 2012
2020 Mathematics Subject Classification: Primary: 60-01 Secondary: 62-01 [MSN][ZBL]
One of the numerical characteristics of a probability distribution. For a real random variable with distribution function
, by a quantile of order
,
, one means the number
for which
,
. If
is a continuous strictly-monotone function, then
is the unique solution of the equation
, that is,
is the function of
inverse to the function
. If
is continuous and
, then the probability of the inequality
, is equal to
. The quantile
is the median (in statistics) of the random variable
. The quantiles
and
are called the quartiles, and
, the deciles. The values of the quantiles for suitable values of
enable one to form an idea about the distribution function.
For example, for the normal distribution (see Fig.)
![]() |
the graph of the function can be drawn from the deciles:
;
;
;
;
;
;
;
;
.
Figure: q076270a
The quartiles of the normal distribution are
and
.
Comments
References
[B] | L. Breiman, "Statistics" , Houghton Mifflin (1973) pp. 231ff MR0359089 Zbl 0289.62001 |
[C] | H. Cramér, "Mathematical methods of statistics" , Princeton Univ. Press (1946) pp. 181; 367 MR0016588 Zbl 0063.01014 |
Quantile. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quantile&oldid=24270