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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What's the asymptotic distribution of $\exp(X_n)$, if $X_n$ is a sequence of asymptotically normally distributed random variables?

Let $(X_n)_{n\in\mathbb{N}} $ be a sequence of asymptotically normally distributed random variables, such that $\lim\limits_{n\to\infty}\sqrt{n}X_n\sim N(0,1)$. What's the asymptotic distribution of $...
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How can I compare an expected value to log transformed data?

For a school project I need to show that the data I was given does not match the expected value found in literature. My data is the diametre of 150 particles and the distribution is pretty close to ...
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Does benfords law imply a log scale for the distribution?

We see Benfords Law in a lot of real world data sets, with the general derivation that if things are distributed symmetrically on a log scale, then the law holds. However, it's not obvious to me: Why ...
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Log-normal distribution probability

Hey I have a very rookie question however, I havn't had statistics in a log time! I have a Log-normal distribution following ~(1,0.6^2). And I would like to find the probability that out of 15 stones, ...
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Comparing Mean and standard deviation from a normalized histogram and scipy.stats.lognormal fit

I am trying to fit a lognormal distribution to my experimental Data. The experimental data provides the frequency of occurrence of a certain length. The data is given in the code below. The counts_exp ...
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ANOVA different p-values on logarithmic and linear scale

I want to compare two groups with one-way anova. I tried to do that using log and linear scale to see if both scales are different one another, and yes the p-values are different. I am using r for ...
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Lognormal model and standard deviation as a measure of variation

I am asking this since my math skills won't allow me to answer this question by myself. I have an outcome variable with the lognormal distribution. Thus, I use the lognormal regression parametrized as ...
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Lognormal model: looking correlations between its re-parametrized estimates (median and SD)?

I analyse the measure of central tendency (median) together with the standard deviation (SD) to examine geographical disparities in the distribution of available resources (y). Y variable is ...
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Skewness of lognormal distribution

Does anyone know how to derive the equation of the skewness of a lognormal distribution? $$\left(\exp(\sigma^2)+2\right)\sqrt{\exp(\sigma^2)-1}$$
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Do I need to sample the distribution in order to apply the central limit theorem?

My scenario is the following: I have a sample set of 1000+ rows, of which my variable of interest is a non-normal distribution. I haven't tested throughtly to check what kind of distribution it is, ...
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Modified Cox method in calculating confidence intervals for Log-Normal distribution

As titled, I want to find confidence intervals for something Log-Normally distributed. I found this paper online that suggests the use of t instead of the usual <...
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Distribution of $\frac{1}{1+X}$ if $X$ is Lognormal

Suppose $Z \sim \mathcal{N}(0,1)$. Suppose $X$ is a lognormally distributed random variable, defined as $X:=X_0exp^{(-0.5\sigma^2+\sigma Z)}$, in other words, $X$ is log-normal with $\mathbb{E}[X]=X_0$...
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Which field of science applies the log-normal sample median distribution?

Which field of science applies the log-normal sample median distribution (i.e. the sample median distribution with samples from a log-normal parent)? I noticed that incubation periods are assumed log-...
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what is the pdf of the ratio of two random log-normal variables

Assume 𝑋,𝑌 are two independent log-normal random variables. What is the distribution of 𝑋/(𝑋+𝑌)?
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Variance of the method of moments estimator for $\mu$ of log-normal distribution

Suppose the data has originated from a log-normal distribution with parameters $\mu$ and $\sigma$ (i.e. the mean and standard deviation of the underlying normal distribution). I have only the sample ...
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Test diffrances of means in zero inflated, non normal distribiution

I have a big number of clients, that can be either treated with and ad (target group) or no (control group). The purchases after set amount of days are drawn from zero inflated (>50% of zeros) ...
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Lognormal model: reporting median or geometric mean

I have a bayesian lognormal model as follows (brms package): m = brm(y ~ 1, data = df, family = lognormal) Model was run with default priors. This is model's ...
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Conditional expection of a lognormal process

Suppose I have the following process $$y_{t+1} = y_t \exp (\varepsilon_{t+1})$$ where $\varepsilon_{t+1}\sim _{iid} N(\frac{\sigma v^2 }{2},v^2 )$, $v> 0$. I would like to calculate $E[y_{t+1}|y_t]$...
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Transformation of confidence limits of Poisson Log linear glmm

I fitted a Poisson log linear model of the form Y ~ poisson(lambda) log(lambda) = mu + beta1X1 + beta2X2 I obtained the estimates and confidence limits ...
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Defining the overlapping area of two log-normal distributions with different means, same variance, and different scaling factors that add up to 1

Define $$ \begin{cases} X_1\sim Lognormal(ln(\mu_1), \sigma^2) \\ X_2\sim Lognormal(ln(\mu_2), \sigma^2) \end{cases} $$ where $\mu_2>\mu_1>0$ and that there is a definite proportion, $\eta\in(0,...
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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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How to prove a variable has a log-normal distribution knowing that the variable is a function of a normal random variable?

Let $X$ be a normal random variable with mean $\mu$ and variance $\sigma^2,\; X\sim N(\mu, \sigma^2).$ Prove that the variable $Y = \exp(X)$ has a log-normal distribution. $$f(y)=\frac{1}{y\sigma\sqrt{...
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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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PDF of a log-normally distributed variable after tangens hyperbolicus transformation

Assume a variable $x_0>0$ with log-normally distributed noise, such that the observation $x$ of $x_0$ has the following PDF: $$ p(x\mid x_0) = \frac{1}{\sqrt{2\pi}\sigma x}e^{-\frac{\left(\ln{(\...
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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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When the number occurences in a time interval are not Poisson distributed?

The lectures statistics I followed also presented the Poisson distribution. We were taught that the number of events occurring in a time interval, that this statistic follows a Poisson distribution. $ ...
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Generating random numbers that are log-normally distributed

Even though I don't quite understand why and how this works, I appreciate how simple it is to generate a set of numbers which are Poisson distributed: ...
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259 views

Is there something like z-value for log-normal distributions?

I'm looking for a reasonable way to measure how unlikely a data point is assuming it's generated by a random variable that follows log-normal. Do we have something like Z-value for normal distribution ...
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Use of Kurtosis statistic for understanding lognormality

To help clarify my understanding of this statistic, I'd appreciate feedback on the rationale presented here. Assume we have a distribution that seems potentially lognormal. Checking the median against ...
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(Regression) Confused with the distributions of fitted values, actual response values and simulated values

I have a dataset with, say, $12000$ observations, $1$ response and $10$ covariates. I want to model this dataset using a Lognormal Regression such that the mean function is given by: $E[Y\vert X]=e^{{...
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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 ...
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Clarification of random variable with lognormal distribution (stocks)

Suppose we have a random variable $S_t$ with a log normal distribution distribution, where $S_t$ represents the price of a stock at a time $t$. Suppose that we have the annual volatility $\sigma$, of $...
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Lognormal GLM and variance estimation

I'm modeling an outcome with a positively-skewed distribution. I have chosen to use a GLM with a lognormal distribution and the identity link. Note: I am not log-transforming the outcome variable ...
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Correlation between normal and log-normal variables

(This is not a homework question.) Let $(X_1 \sim N(\mu_1,\sigma_1), X_2 \sim N(\mu_2, \sigma_2))$ be a bivariate normal random variable with the correlation between $X_1$ and $X_2$ given by $\rho$. ...
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How to calculate `mean` and `sd` of lognormal distribution based on `meanlog` and `sdlog`? [duplicate]

Lognormal distribution as below: estimate meanlog 6.0515 sdlog 0.3703 How to calculate the mean and <...

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