Cross Validated Asked by Soham Bagchi on December 8, 2020

I’m trying to derive the estimators of the parameters using maximum likelihood method for Weibull distribution in random censoring scheme

$f(t)=alphalambda(lambda t)^{alpha -1}e^{{-lambda t}^{alpha}}$,$alpha >0$,$lambda>0$

Now i reparametrize $gamma=lambda^{alpha}$

then $f(t)=gammaalpha t^{alpha-1} e^{-gamma t^{alpha}}$

here $n_{u}$=number of uncensored observations

So the survival function $S(t)=e^{-gamma t^{alpha}}$

L=$(gamma alpha)^{n_{u}}$ $(prod_{u} t_{i} ^{alpha-1})$ exp{$-gamma sum_{u}t_{i} ^{alpha}$} exp{$-gamma sum_{c} c_{i} ^{alpha}$},

=$(gamma alpha)^{n_{u}}$($prod_{u} t_{i} ^{alpha -1} $)exp{$-gamma sum_{i=1}^n y_{i} ^{alpha} $}

Then

log L=$n_{u}log gamma$ + $n_{u} log alpha$ + $(alpha -1) sum_{u} log t_{i}$ + $gamma sum_{i=1}^n y_{i} ^{alpha}$

So,

$frac{partial}{partial gamma}log L=frac{n_{u}}{gamma}-sum_{i=1}^n y_{i} ^{alpha}$

$frac{partial}{partial alpha}log L=frac{n_{u}}{alpha}+sum_{u} log t_{i}- gammasum_{i=1}^n y_{i} ^{alpha} log y_{i}$

Now to write a program in R and to simulate the results,I need to obtain equations for $hat{alpha}$ and $hat{gamma}$ in the form to solve NR method.

**Suggest me a way to proceed**

1 Asked on November 12, 2021

machine learning precision recall random forest unbalanced classes

1 Asked on November 12, 2021

1 Asked on November 12, 2021

1 Asked on November 12, 2021

binary data classification precision recall unbalanced classes

0 Asked on November 12, 2021 by vineet

0 Asked on November 12, 2021

1 Asked on November 12, 2021 by stephen-clark

1 Asked on November 12, 2021 by user6703592

0 Asked on November 12, 2021

1 Asked on November 12, 2021 by emma-jean

0 Asked on November 12, 2021 by rbeginner

1 Asked on November 12, 2021

1 Asked on November 12, 2021

cox model mathematical statistics r survival time varying covariate

2 Asked on November 9, 2021 by jennifer-ruurs

1 Asked on November 9, 2021 by joy_1379

1 Asked on November 9, 2021 by astel

errors in training hyperparameter supervised learning tuning

Get help from others!

Recent Answers

- Joshua Engel on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- haakon.io on Why fry rice before boiling?

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP, SolveDir