The exponential pdf is a measure of lifetimes of devices that do not age (see Question 3.11.11). However, the exponential pdf is a special case of the Weibull distribution , which can measure time to failure of devices where the probability of failure increases as time does. A Weibull random variable Y has pdf f Y ( y ; α , β ) = α β y β − 1 e − α y β , 0 ≤ y , 0 < α , 0 < β . Find the maximum likelihood estimator for α assuming that β is known.
The exponential pdf is a measure of lifetimes of devices that do not age (see Question 3.11.11). However, the exponential pdf is a special case of the Weibull distribution , which can measure time to failure of devices where the probability of failure increases as time does. A Weibull random variable Y has pdf f Y ( y ; α , β ) = α β y β − 1 e − α y β , 0 ≤ y , 0 < α , 0 < β . Find the maximum likelihood estimator for α assuming that β is known.
The exponential pdf is a measure of lifetimes of devices that do not age (see Question 3.11.11). However, the exponential pdf is a special case of the Weibull distribution, which can measure time to failure of devices where the probability of failure increases as time does. A Weibull random variable
Y
has pdf
f
Y
(
y
;
α
,
β
)
=
α
β
y
β
−
1
e
−
α
y
β
,
0
≤
y
,
0
<
α
,
0
<
β
. Find the maximum likelihood estimator for α assuming that
β
is known.
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
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Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License