Quantiles
smallest
Example:the 90th percentile (0.9th quantile) is the
number such
thatP1 X the number) > 0.9.
pth ele
This is the
↓ These are
population A quail
-
quantiles.
sample percentiles
pi
y)+17 (
=
↑Holy
quantiles:
-
①p
What's the difference between percentiles and quantiles?
Quantiles will be decimals
(e.g. 0.5th quantile) whereas percentiles will be
the quantile 100
x
(eg. 50th percentile).
Normal Distribution
pdf fy(y)
tep( z(y-M(]j
>
=
-
a
c
-
-
# ai2 ( z(-+ y]/ -
, Uniform distribution
(ar0
oz e
For X -unif (0,02):fx(x) =
otherwise
Fx(x)
2 -
Op
formula.
=
think
- ofthe linear interpolation
O2-0,
E(x) P,
VarIX)=(O-d
0,
=
+
-
average
8
for e
Y-gamma(a.), fy(y)
-
Gamma distribution -
y
=
,y>0
BYT(x)
Note thatP (x) (a -1)! (x 1)4(x 1)!
=
= -
-
E(Y) =
a
B and Var(Y) a
=
&2
smallest
Example:the 90th percentile (0.9th quantile) is the
number such
thatP1 X the number) > 0.9.
pth ele
This is the
↓ These are
population A quail
-
quantiles.
sample percentiles
pi
y)+17 (
=
↑Holy
quantiles:
-
①p
What's the difference between percentiles and quantiles?
Quantiles will be decimals
(e.g. 0.5th quantile) whereas percentiles will be
the quantile 100
x
(eg. 50th percentile).
Normal Distribution
pdf fy(y)
tep( z(y-M(]j
>
=
-
a
c
-
-
# ai2 ( z(-+ y]/ -
, Uniform distribution
(ar0
oz e
For X -unif (0,02):fx(x) =
otherwise
Fx(x)
2 -
Op
formula.
=
think
- ofthe linear interpolation
O2-0,
E(x) P,
VarIX)=(O-d
0,
=
+
-
average
8
for e
Y-gamma(a.), fy(y)
-
Gamma distribution -
y
=
,y>0
BYT(x)
Note thatP (x) (a -1)! (x 1)4(x 1)!
=
= -
-
E(Y) =
a
B and Var(Y) a
=
&2
