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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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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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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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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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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1answer
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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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Mixture of Gaussians on Log of Data

I am practicing Mixture of Gaussians and found the below dataset snoq, which is the precipitation amounts recorded at a US region, with ...
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The distribution of the product of a multivariate normal and a lognormal distribution

If $$X=\left(\begin{array}{c} X_{1}\\ X_{2} \end{array}\right)\sim N\left[\left(\begin{array}{c} \mu_{X_{1}}\\ \mu_{X_{2}} \end{array}\right),\left(\begin{array}{cc} \sigma_{X_{1}}\\ \sigma_{X_{1}X_{2}...
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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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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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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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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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Calculating standard deviation from log-normal distribution confidence intervals

I have the results of a meta-analysis of 10 studies that reports a combined random effects odds ratio (computed using Woolf's method) and 95% confidence interval of an event happening in one group ...
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What is the best point forecast for lognormally distributed data?

I believe that the values I am forecasting are lognormally distributed with log-mean $\mu$ and log-variance $\sigma^2$. I need a point forecast (i.e., a one-number summary) that minimizes the expected ...
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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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Data normalization for linear regression

I'm currently writing my thesis on the comparison of ultrasound measurements with DEXA scan measurements for specific fat distributions (40 participants). I would like to perform a linear regression ...
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1answer
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Justification for use of non-conjugate priors?

Google searches gives no results to this question and there is the opposite question in this site, which makes me think this has an intuitive response I am missing. In most course notes and responses ...
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Mixture model for a mix of normal and lognormal distributions in R

I have a distribution composed of a mixture of a normal distribution and a log-normal distribution. A simulated example that looks quite similar to what I will expect in the real data would be: ...
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Interpreting the difference between lognormal and power law distribution (network degree distribution)

First off, I'm not a statistician. However, I have been doing statistical network analysis for my PhD. As part of the network analysis, I plotted a Complementary Cumulative Distribution Function (...
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Appropriate to fit lognormal model to data with heavy tail?

I am attempting to standardize recreational fishery CPUE data. I am using a delta approach, with a binomial model fit to the presence/absence data and a lognormal model fit to the positive ...
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Showing the expectation of a lognormal AR(1) process

Suppose I have a lognormal AR(1) process: $$\log(y_{t+1}) = (1-\theta)c + \theta \log (y_t) + \varepsilon_{t+1},$$ $$\varepsilon \sim N(0,\sigma^2)$$ To show $\operatorname{E}(y_{t+1})$, is it ...
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Proportional hazards model with lognormal baseline hazard in R?

I would like to fit a proportional hazards model with log normal baseline hazard in R. I have found several options for the semiparametric Cox proportional hazards, but I have not found a package to ...
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Impact of correlation bounds for Monte Carlo simulations

As the lognormal distribution imposes bounds of attainable correlations as discussed in Attainable correlations for lognormal random variables my question would be what happens if say we want to do a ...
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Lognormal distribution correlation bounds on monte carlo simulations of the minimum variance hedge ratio

As the lognormal distribution imposes bounds of attainable correlations as discussed in Attainable correlations for lognormal random variables my question would be what happens if say we want to do a ...
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Survivor function for log-normal from flexsurvreg output

I am trying to plot/generate a survival curve in Excel using the output from flexsurvreg in R. The below is a snapshot from R with the corresponding estimates (y axis values) for the time (x axis ...
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Expected value of a sum of random variables raised by $e$?

There is a function $y$ defined $$y=\exp(-\boldsymbol{\alpha}'\mathbf{b})\:\:;\:\:\:\:y\in(0,\infty)$$ where $\boldsymbol{\alpha}$ is a vector of random variables and $\mathbf{b}$ is a vector of non-...
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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 ...
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Probability for the Quotient of two lognormal distributions (Analytical vs Monte Carlo)

I am struggling on a problem for some time now and any help would be highly appreciated. From an "easy" problem, known to have a closed-form solution, I find strange the existence of such a huge ...
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what is the distribution of the log of a normal distribution? [duplicate]

if you exponentiate a normal distribution, Y=exp{X} where X is a normally distributed random variable (RV), then Y is log-normally distributed. What is the ...

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