arXiv subjects

Samuel Forbes

Publications and source records attributed to Samuel Forbes.

5 recordsLinked to original sources

arXiv2026

UK Income Inequality and Taxation, 2000--2023: A $\kappa$-generalised Distribution Analysis

We analyse the UK income distribution from 2000 to 2023 using HMRC annual percentile data for both pre-tax and post-tax income. We fit a prefactor-adjusted $\kappa$-generalised specification to the data by weighted non-linear least squares and use inverse transform sampling to generate simulated income populations. The results suggest a redistribution of income shares over the period: the bottom 40\% appears to have increased its share, the middle-upper part of the distribution (50th--90th percentiles) lost share, the top 10\% remained broadly stable, and the top 1\% increased its share of pre-tax income. Because the modified specification is defined only above a positive threshold, conclusions concerning the lower tail should be interpreted with some caution. Using simulated 2023 pre-tax incomes to examine tax reform scenarios, we find that revenue-equivalent tax increases on high-income earners must be more than four times as large as comparable increases on lower-income earners. This suggests that, despite increased concentration at the top, the UK tax base remains driven primarily by the large number of taxpayers outside the very top of the distribution.

econ.EM↗

arXiv2024

The $\kappa$-generalised Distribution for Stock Returns

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the $\kappa$-exponential function that is asymptotically exponential for small values and asymptotically power law for large values. This proves to be a useful property and makes it a good candidate distribution for many types of quantities. In this paper we focus on fitting historic daily stock returns for the FTSE 100 and the top 100 Nasdaq stocks. Using a Monte-Carlo goodness of fit test there is evidence that the $\kappa$-generalised distribution is a good fit for a significant proportion of the 200 stock returns analysed.

q-fin.ST↗

arXiv2023

Linear Regression for Power Law Distribution Fitting

We fit the exponent of the Pareto distribution, that is equivalent or can approximate the continuous power law distribution given a cutoff point, using linear regression (LR). We use LR on the logged variables of the empirical tail (one minus the empirical cumulative distribution function). We find the distribution of the consistent LR estimator and an approximate sigmoid relationship of the mean that underestimates the exponent. By factoring out a sigmoid function used to approximate the mean we transform the LR estimator so it is approximately unbiased with variance comparable to the minimum variance unbiased transformed MLE estimator.

stat.AP↗

arXiv2023

A Study of the Probability Distribution of the Balls in Bins Process with Power Law Feedback

We analyse the balls in bins process with feedback with primary focus on the power law feedback function $f(\omega)=\eta \omega^{\gamma}\,$, $\eta>0\,$ $\gamma \geq0\,$. Using the recursive solution to the master equation we find for power law feedback numerical evidence that the probability mass function for finite time scales asymptotically with $\omega^{-\gamma}\,$ for $\gamma>1\,$. We also provide simulations supporting a previous result by Oliveira (corollary to Theorem 4 in \cite{oliveira2009onset}) that the tail of the losers scale as $\omega^{-(\gamma-1)}\,$ but extending to $N \geq 2$ bins. We thus find evidence that the balls in bins process with power law feedback produces power law distributions as is common to many real world phenomena.

math.PR↗

arXiv2021

A Study of UK Household Wealth through Empirical Analysis and a Non-linear Kesten Process

We study the wealth distribution of UK households through a detailed analysis of data from wealth surveys and rich lists, and propose a non-linear Kesten process to model the dynamics of household wealth. The main features of our model are that we focus on wealth growth and disregard exchange, and that the rate of return on wealth is increasing with wealth. The linear case with wealth-independent return rate has been well studied, leading to a log-normal wealth distribution in the long time limit which is essentially independent of initial conditions. We find through theoretical analysis and simulations that the non-linearity in our model leads to more realistic power-law tails, and can explain an apparent two-tailed structure in the empirical wealth distribution of the UK and other countries. Other realistic features of our model include an increase in inequality over time, and a stronger dependence on initial conditions compared to linear models.

econ.TH↗