# Questions tagged [lognormal]

A lognormal distribution is the distribution of a random variable whose logarithm has a normal distribution.

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### Correlation of lognormal processes

Proposition: If X(t) is a lognormal process then corr(X(t),1/X(t))=-1. What is a lognormal process? What are the differences between a lognormal process and a lognormal distribution? Can anybody ...
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### Why clustering in a linear scale using correlation based distance gives better results than clustering in a log2 scale?(PAM clustering)

I have questions regarding cluster analysis. I am trying to cluster data made up of proteins. (23 columns and 1800 rows) I have the data in a log2 scale, some variables range between 2-10 and others ...
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### Fitting a lognormal-pareto distribution to empirical data distribution in R

Let's say I have data whose distribution is leptokurtic, with a lognormal peak and a pareto tail (for this question, I will generate lognormal-pareto data using package CompLognormal but I will need ...
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### Transformation of data with zero and R squared

I have a conceptual concern about data tranformation and R^2. Often we transform data to respect the assumption of the linear model. Therefore, we can use multiple type of transformation such as log ...
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### Fraction below threshold across a population with individual variation, i.e. thinking about food

For an individual, a parameter is known to follow a lognormal distribution:  $log(x_i) \sim Normal(\mu_i, \sigma_i)$ For a population, $\mu$ and $\sigma$ are known to follow a bivariate lognormal ...
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### Difference of two i.i.d. lognormal random variables

Let $X_1$ and $X_2$ be 2 i.i.d. r.v.'s where $\log(X_1),\log(X_2) \sim N(\mu,\sigma)$. I'd like to know the distribution for $X_1 - X_2$. The best I can do is to take the Taylor series of both and ...
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### Any known approximations of summing quantiles from joint (bernoulli / lognormal) distributions

This is my first post to this site! For an insurance-like scenario, I have several independent risks which I want to sum together and find a 95% percentile. Currently I do this by Monte Carlo but I ...
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### How to determine the distribution of a parameter fit by nonlinear regression

The example above shows enzyme kinetics -- enzyme velocity as a function of substrate concentration. The well-established Michaelis-Menten equation is: $Y=V_{max} \cdot \dfrac{X}{K_m + X}$ $X$ are ...
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### Contrasts for distributional parameters in a shifted log normal distrbution

I’m playing around with shifted log normal distributions in brms (for reaction time data), trying to get my head around the parameter estimates and also how to do contrasts with them using the emmeans ...
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### Expectation of log skew normal distribution

What is the expected value and expected variance of a log skew normal distribution? In case I have the terminology wrong, I'm referring to data that is lognormal with some skew mild skew when it's log ...
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### Expectation of a type of bivariate lognormal

Suppose $S_1 \sim e^\mathbf{X}$ where $\mathbf{X} \sim N(\mu, \mathbf{\Sigma})$, $\mathbf{X}$ is a bivariate normal distribution then what is the following, $$E\left[ \theta_1^\intercal S_1 \right]$$...
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### Numerically Solve for Parameters Characterizing Lognormal RV that's Truncated from Above

I am trying to numerically solve for parameters characterizing a lognormal distribution truncated from above with first moment = mean, second moment = ...
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### 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.!
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### Estimating Population Total of a Lognormal distribution

Say we’re trying to model spending behavior and it has a lognormal distribution, lognormal(6.4, 0.8) with N=1000 independent observations, a vector named A. What’s the expected value of the total ...
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### absence of normality of residuals - lmer or glmer?

I am in the process of analysing response time data and after inspection of the response times (as expected) they were not normally distributed, so I applied a log transformation which I know is not ...
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### Undefined MGF but all moments finite?

For the lognormal distribution: https://en.wikipedia.org/wiki/Log-normal_distribution The moment generating function is undefined, but all the moments exist and are finite. I thought the moment ...