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Questions tagged [calculus]

For statistical questions involving calculus. Please use also a more statistical tag. For purely mathemathical questions about the calculus, it is better to ask at math SE https://math.stackexchange.com/

3
votes
1answer
96 views

Finding integral of minimum function. yn(1-y)^(n-1)

This is for a homework question in which I am trying to find the $E(Y_n = min\{X_1,...,X_n\}$). So far I have found that the minimum cdf, as below. The minimum of $X_i$ is when all of $X_i > x$. ...
0
votes
1answer
25 views

What is the right method to estimate rate of change in daily values over a period of time?

I would like to ask you what is the best (or the right way) to calculate the rate of change in air temperature over a period of time and then see how this rate changes over time. Daily air temperature ...
0
votes
1answer
145 views

Is there local minimums in MSE function?

Here is "mean squared error" function: C = $\frac{1}{2n}$ * $\sum(length(y - a)^2)$ As I understand, this is like paraboloid in multidimensional space. So, I guess, there is only one extremum: global ...
-1
votes
1answer
505 views

How to differentiate the distribution function of lognormal distribution with respect to its parameters?

How to differentiate the distribution function of lognormal distribution with respect to its parameters? What solution will we get? I know if differentiate wrt variable, we will get density function.!
-1
votes
1answer
67 views

Transformation of random variables in Generative Adversarial Nets

Let $x$ and $z$ be real-valued random vectors, where $x = g(z)$, and $g$ is an invertible, continuous and differentiable transformation of $z$. Then $p_z(z) = p_x(g(z)) \lvert det(\frac{\partial g(z)}{...
5
votes
0answers
2k views

Deriving linear regression gradient with MSE

So I've been tinkering around with the backpropagation algorithm and to try to get a better understanding of how it works and my calculus is quite rusty. I've derived the gradient for linear ...
1
vote
0answers
39 views

Solving integrals in R

I would like to write an R function for solving the following equation: Essentially I would like to be able to set or vary the parameters values of "m" and "s" and those parameters in "p(t)" ...
1
vote
0answers
22 views

Verifying sub-exponential property when a random variable is not sub-gaussian pro

I am referring to the Example 2.4 (page 16) in this book chapter https://www.stat.berkeley.edu/~mjwain/stat210b/Chap2_TailBounds_Jan22_2015.pdf Suppose $Z \sim N(0,1)$ and random variable $X=Z^2$. ...
1
vote
0answers
15 views

Maximize profits by setting price

I am working on a model to set a price that maximizes profits. The equation for profits is: Profits=price x (# sold) - (fixed cost) x (# sold) I have models ...
1
vote
0answers
43 views

Can Regularization by achieved using Relative Sensitivity?

In a Mathematical Model we measure the sensitivity of the output with respect to the parameters and it is desirable that a small change in a parameter doesn't lead to wild fluctuations in the output ...
1
vote
0answers
478 views

Meaning of Jacobian of the transformation for pdf of function of random vectors

I am studying multivariate statistics and I don't understand the meaning of Jacobian of the transformation for pdf of function of random vectors. If I have a random vector, let's say bivariate, (X,Y)...
1
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0answers
108 views

Solution verification - calculation of second derivatives of multinomial probit log-likelihood function

The initial function of log-likelihood of multinomial probit model with $J$ alternatives: $ ln \ell=\sum_{i=1}^N\sum_{j=1}^{J-1} y_{ij} \cdot ln \Phi(\sum_{k=1}^Kx_{ik}\beta_{kj})+ ({n_i-\sum_{j=1}^{...
0
votes
0answers
21 views

Conditional Density Estimate Loss. Why the double integral?

I read RFCDE: Random Forests for Conditional Density Estimation. Just like it sounds, these folks trained random forests for making conditional density estimates. At inference time, density estimates ...
0
votes
0answers
31 views

How to manually calculate odds ratio for continuous variables?

In school, long before learning about logistic models, I've been taught how to calculate odds ratios by hand. Formula was based on a contingency table, just like this: This is very easy to ...
0
votes
0answers
9 views

Threshold optimization with two parameters where first parameter need to be minimum and second value to be maximum

We have threshold values ranging from 1 to 10 where attributes p1, p2 increase with increase in threshold. Our intention is to find threshold with minimum p1 and maximum p2. It would be of great help ...
0
votes
0answers
28 views

Re-express the lognormal density in terms of its mean value

I wonder if it is possible to rewrite the lognormal density function, $$f(x)=\frac 1 {x\sigma\sqrt{2\pi}}\exp\bigg(-\frac{(\log x-\mu)^2}{2\sigma^2}\bigg)$$ so that the mean value, $\exp(\mu+\frac{ \...
0
votes
0answers
56 views

Simplifying equation involving logit function

I have an equation obtained from inverse logit transformations $$\left(1+e^{-(\tilde{\alpha}+x_1\tilde{\beta_1})}\right)^{-1} = (1-\phi)\left(1+e^{-(\alpha+x_1\beta_1)}\right)^{-1}+ \phi\left(1+e^{-(\...