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This paper proposes and implements a methodology to fit a seven-parameter Generalized Tempered Stable (GTS) distribution to financial data. The nonexistence of the mathematical expression of the GTS probability density function makes maximum-likelihood estimation (MLE) inadequate for providing parameter estimations. Based on the function characteristic and the fractional Fourier transform (FRFT), we provide a comprehensive approach to circumvent the problem and yield a good parameter estimation of the GTS probability. The methodology was applied to fit two heavy-tailed data (Bitcoin and Ethereum returns) and two peaked data (S&P 500 and SPY ETF returns). For each historical data, the estimation results show that six-parameter estimations are statistically significant except for the local parameter, μ. The goodness of fit was assessed through Kolmogorov–Smirnov, Anderson–Darling, and Pearson's chi-squared statistics. While the two-parameter geometric Brownian motion (GBM) hypothesis is always rejected, the GTS distribution fits significantly with a very high p-value and outperforms the Kobol, Carr–Geman–Madan–Yor, and bilateral Gamma distributions. [ABSTRACT FROM AUTHOR]

Objective: Mental health and arthritis have been recognized as major public health issues. Francophone minority status has now been acknowledged as a health determinant. The objective of this study was to determine the prevalence of major depression among adults with arthritis in Francophone minority populations compared to the Anglophone majority., Methods: Secondary analysis of the CCHS (merger of 2003 (cycle 2.1), 2005 (Cycle 3.1), 2007 (cycle 4.1), 2008 and 2009) excluding Quebec residents. The language variable was constructed using an existing algorithm which combines maternal tongue, language of conversation, language of interview, and preferred language. Major depression was defined according to the DSM IV. Presence or absence of arthritis was a self-reported variable. The prevalence and odds ratios for depression in people with arthritis were calculated and adjusted for various factors (socio-economic, social isolation, access to health services)., Results: The study identified 159,426 Anglophones and 10,658 Francophones. Among the participants with arthritis (27%), the prevalence of depression in Francophones and Anglophones was 8.5% and 8.4%, respectively. In men, Anglophones were more at risk for depression than Francophones: OR 2.36 (95% CI: 2.07-2.70) vs. OR 1.87 (95% CI: 1.20-2.91). This trend was not observed in women., Conclusion: In our sample of people with arthritis, depression seems to affect more particularly the English-speaking men, however given the small sample size, we need to be cautious in our conclusions.