Binomial distribution: in the exponential family

[@LaurenChapa]

i am so grateful for your videos, this is the first time i have fully comprehended this subject. thank you for sharing!

[@mrlmaokun]

This is still useful 8 years on, thank you so much.

[@oliviacummings2112]

Thank you for this video!! Super helpful and well explained!

[@yuqianchen7820]

Really helpful by doing all the steps so clearly!! All series about the exponential family is so awesome, a lot of help for my exams

[@MiyadhIslamNup]

❤❤

[@buu2]

Thank you for this clear step-by-step explanation.

[@ViniciusAngeloraniero]

You saved my life

[@NiklasLandsberg-i1u]

Super helpful!

[@actuariallyspeaking7692]

Thank you sooo much for this

[@Shahzaib-oe9jn]

your work is amazing ma'am , i love you so much

[@sergiomwendwa809]

Thank you so much madam professor.

[@MOHSINALI-bk2qo]

can you plz tell me how this e^theta/1+e^theta comes? plz help with this OR give it any reference

[@Siroitin]

multiply, expand, subtract and divide

[@silas3463]

Very informative, thank you!

[@muhammadsulaman5426]

Thnk you ❤❤

[@scarfacek]

Brilliant video

[@omarhaque7194]

n is another parameter in the model, why can you take that into b(theta)?

[@harrisonmorgan5139]

Omar Haque you can, the parameterisations are not unique

[@youtubeadventurer1881]

It looks like you're using a bit of a funky form of the exponential family there. In all the sources I've seen it's been the exponential function of a dot product of the natural parameters and the sufficient statistics and then two separate functions of the parameters and the variable respectively, either within the exponential function or multiplying the exponential function. Am I missing something?

[@deetoher]

Its a form of the natural exponential family (a subset of the exponential family) which then leads onto having canonical link functions - I use these as part of a course on generalised linear models.

[@youtubeadventurer1881]

@@deetoher Oh I see, thank you for clearing that up.

[@Ragnarik17]

@@deetoher please excuse my dumbness. But how can you get exp(theta) /(1+exp(theta))

[@jayjayf9699]

I don’t know why we have to write in the exponential family form , where did this form come from ?

[@deetoher]

For other distributions it is more obvious, as it is all in one video rather than split into two. Writing it in this form allows us to find the canonical link function, which is a mapping used when you are using generalized linear models. For the binomial distribution, this is the logit function (hence "logistic" regression). As a byproduct, it also allows the mean and variance to be easily calculated (but that is more relevant for distributions such as the Normal distribution or the gamma distribution, where the integration calculations are horrible).

[@jayjayf9699]

@@deetoher thank you

[@jLaihm1]

explained very clearly ty ;D

[@garymikelastorgaaguero3669]

Thank you so much

[@FederationStarShip]

Thank you for this.

[@BluePuppy210]

Thank you so much!!!

[@harrietfosuahquansah4180]

Great video 😊 Please when the expression nlog(1-p) was expressed in terms of theta it turned negative that is -nlog(1+e^theta) and the b theta function is being subtracted from x theta, so by substitution the negatives should turn positive... Kindly clarify that portion for me. Thank you.

[@norahalraddadi8540]

Thank you !!!!

[@clonetrooper5674]

thank you

[@tianyouliu178]

Thanks

[@1fai377]

Why did you write f(y)

[@deetoher]

Because it emphasises that this is a function - the letter you use doesn't matter. So I highlight that you are comparing to a "form" of how the distribution (which is just a function of a variable) is written.

[@1fai377]

deetoher Thank you

[@ronaldhernandez7802]

I love u

[@nondogopal1251]

Thanks