# Investigating Multiwavelength Lognormality with Simulations—Case of Mrk 421

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## Abstract

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## 1. Introduction

## 2. Observations and Data

## 3. PDF Estimation Methodology

## 4. Results: Normal vs. Lognormal

## 5. Discussion and Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Figure shows the histogram of the observed Fermi-LAT lightcurves compared to those for simulations. Using simulations confidence intervals (dashed red) are derived at the 1$\sigma $ level for each bin. (

**a**) Simulations of the fluxes that are normally distributed. (

**b**) Simulations of the logarithm of fluxes that are normally distributed or lognormal simulations. The lognormal simulations fit the lightcurves significantly better with SW p-values of $0.013$ relative to $1.78\times {10}^{-14}$ or $p\ll 0.001$ for the normal case.

**Figure 2.**Similar to Figure 1 for BAT lightcurves. Both (

**a**) normal simulations and (

**b**) lognormal ones are not great fits with SW p-values of $8.29\times {10}^{-16}$ (i.e., $p\ll 0.001$) and $1.30\times {10}^{-6}$ (also, $p\ll 0.001$), even though the latter appears to be better. This mismatch is potentially due to the multi-modal, bursty structure.

**Figure 3.**Similar to Figure 1 for OVRO lightcurves. Between (

**a**) normal simulations and (

**b**) lognormal ones, the normal distribution is a somewhat better fit with SW p-values of $2.31\times {10}^{-4}$ relative to $4.80\times {10}^{-6}$. Once again the multi-modal, bursty structure makes it complex to explain with a single model for PDF.

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**MDPI and ACS Style**

Chakraborty, N. Investigating Multiwavelength Lognormality with Simulations—Case of Mrk 421. *Galaxies* **2020**, *8*, 7.
https://doi.org/10.3390/galaxies8010007

**AMA Style**

Chakraborty N. Investigating Multiwavelength Lognormality with Simulations—Case of Mrk 421. *Galaxies*. 2020; 8(1):7.
https://doi.org/10.3390/galaxies8010007

**Chicago/Turabian Style**

Chakraborty, Nachiketa. 2020. "Investigating Multiwavelength Lognormality with Simulations—Case of Mrk 421" *Galaxies* 8, no. 1: 7.
https://doi.org/10.3390/galaxies8010007