# Questions tagged [lognormal]

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

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### How to prove a distribution is or is not heavy tailed?

I've seen the definition for a distribution that has a heavy right tail but I can't seem to prove to myself that a distribution has a heavy right tail or not. How would you prove that for the normal ...
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### Distribution that relates mean and standard deviation with positive support

I am working on a meta analysis that is looking at change in dopamine levels between two populations. I have the mean and standard deviation for each group along with some trials which are missing the ...
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### characteristic function of standard lognormal distribution

What is the characteristic function of standard lognormal distribution? By "$X$ yields the standard lognormal distribution", I mean $\log(X)\sim N(0,1)$. I understand that the moments of $X$ ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### Fitting a sample streamflow data to log-normal distribution

So I'm a beginner at python and I have a streamflow data for 132 months and I need to fit every months streamflow data to lognormal distribution and finally plot the original data and fitted data on ...
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### change support for dlnorm in R

I am using dlnorm() as a jumping kernel in R for a parameter with range $(0,\infty]$. However, the issue is that the range of the log-normal distribution includes ...
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### Why does the log transformation bring data closer to normal distribution? [duplicate]

Quite often in published research we see researchers apply log transformation to their data, and some claim that this makes the data closer to normal distribution. My questions are: Mathematically, ...
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### How to estimate parameters and pdf of a random variable transformed from a lognormal random variable?

I have a continuous random variable Y that follows lognormal distribution with known parameters (mu and sigma). Let Y be transformed to X=Y-20000. So it is basically shifted to left. How do I find the ...
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### In the poweRlaw package, is the location parameter estimated for a lognormal distribution the $median=\exp(\mu)=\theta$ or $\mu$?

I have a set of graphs (each with the same nodes but with edges' weights defined by different research subjects) for which I would like to report statistics. One of these statistics is the betweenness ...
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### Identifying the best distribution to this data?

I'm trying to fit an appropriate distribution to a data with 216 values and estimate parameters. From Cullen and Frey graph, it looks like lognormal could be a good fit. From q-q plot, Weibull seems ...