Logarithmic Series Research Articles

Detection limit of Mycobacterium chimaera in water samples for monitoring medical device safety: insights from a pilot experimental series

A growing number of Mycobacterium chimaera infections after cardiosurgery have been reported by several countries. These potentially fatal infections were traced back to contaminated heater-cooler devices (HCDs), which use water as a heat transfer medium. Aerosolization of water contaminated with M.chimaera from HCDs enables airborne transmission to patients undergoing open chest surgery. Infection control teams test HCD water samples for mycobacterial growth to guide preventive measures. The detection limit of M.chimaera in water samples, however, has not previously been investigated. To determine the detection limit of M.chimaera in water samples using laboratory-based serial dilution tests. An M.chimaera strain representative of the international cardiosurgery-associated M.chimaera outbreak was used to generate a logarithmic dilution series. Two different water volumes, 50 and 1000mL, were inoculated, and, after identical processing (centrifugation, decantation, and decontamination), seeded on mycobacteria growth indicator tube (MGIT) and Middlebrook 7H11 solid media. MGIT consistently showed a lower detection limit than 7H11 solid media, corresponding to a detection limit of ≥1.44×104cfu/mL for 50mL and ≥2.4cfu/mL for 1000mL water samples. Solid media failed to detect M.chimaera in 50mL water samples. Depending on water volume and culture method, major differences exist in the detection limit of M.chimaera. In terms of sensitivity, 1000mL water samples in MGIT media performed best. Our results have important implications for infection prevention and control strategies in mitigation of the M.chimaera outbreak and healthcare water safety in general.

Research on the Effect of Chinese Margin Trading on Market Risk: Based on GJR Model and Filtered Historical Simulation

In this paper, we address the issue that the financial institutes need to identify the risk of margin trading, and we analyze the volatility and value at risk of China’s Shanghai-Shenzhen 300 Index before and since the inception of margin trading policy. We first analyze the statistical attributes of the logarithmic return series. Then we build the GJR-GARCH to model the difference of volatility and leverage effect of the two sample time series. After that, we calculate the dynamic value at risk based on the parametric method. Moreover, we apply the filtered historical simulation with the help of Bootstrap technique to obtain the pathway of return and finally calculate the value at risk under the two circumstances. In the end, we propose some reasonable policies to financial risk management department.

On generalized logarithmic series distribution and its application to leaf spot grades in mulberry

The generalized logarithmic series distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi-square and weighted discrepancies. The GLSD was fitted to different leaf spot grades in four varieties of mulberry namely Ichinose, Gosherami, Rokokuvoso and Kokuso-20 and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.

Risk and Dependence Analysis of Australian Stock Market - The Case of Extreme Value Theory

The quantification of risk and dependence are major components of financial risk modelling. Financial risk modelling frequenty uses the assumption of a normal distribution when considereing the return series which makes modelling easy but is inefficient if the data is not normally distributed or if it exhibits extreme tails. When dealing with extreme financial events to quantify extreme market risk, Extreme Value Theory (EVT) proves to be a natural statistical modelling technique of interest. Estimation of tail dependence between financial assets plays a vital role in various aspects of financial risk modelling including portfolio theory and hedging amongst applications. Extreme Value Theory (EVT) provides well established methods for considering univariate and multivariate tail distributions which are useful for forecasting financial risk or modelling the tail dependence of risky assets. In this paper we focus on the extreme risk and dependence analysis of the ASX-All Ordinaries (Australian) stock market using using univariate and multivariate EVT based methods. The empirical evidence shows that EVT can be successfully applied to financial market return series for predicting daily VaR using a GARCH(1,1) and EVT based dynamic approach. We also use nonparametric measures based on bivariate EVT to investigate asymptotic dependence and estimate the degree of tail dependence of the ASX-All Ordinaries daily returns with four other international markets, viz., the S&P-500, Nikkei-225, DAX-30 and Heng-Seng for both right and left tails of the return distribution in extreme quantiles. It is investigated whether the asymptotic dependence between these markets is related to the heteroskedasticity present in the logarithmic return series using GARCH filters. The empirical evidence from bivariate EVT methods show that the asymptotic dependence between the extreme tails of the stock markets does not necessarily exist and rather can be associated with the heteroskedasticity present in the financial time series of the various stock markets.

Tail dependence analysis of stock markets using extreme value theory

ABSTRACTFinancial risk modelling frequently uses the assumption of a normal distribution when considering the return series which is inefficient if the data is not normally distributed or if it exhibits extreme tails. Estimation of tail dependence between financial assets plays a vital role in various aspects of financial risk modelling including portfolio theory and hedging amongst applications. Extreme Value Theory (EVT) provides well established methods for considering univariate and multivariate tail distributions which are useful for forecasting financial risk or modelling the tail dependence of risky assets. The empirical analysis in this article uses nonparametric measures based on bivariate EVT to investigate asymptotic dependence and estimate the degree of tail dependence of the ASX-All Ordinaries daily returns with four other international markets, viz., the S&P-500, Nikkei-225, DAX-30 and Heng-Seng for both extreme right and left tails of the return distribution. It is investigated whether the asymptotic dependence between these markets is related to the heteroscedasticity present in the logarithmic return series using GARCH filters. The empirical evidence shows that the asymptotic extreme tail dependence between stock markets does not necessarily exist and rather can be associated with the heteroscedasticity present in the financial time series of the various stock markets.

Using Cuckoo Algorithm for Estimating Two GLSD Parameters and Comparing it with Other Algorithms

This study introduces and compares different methods for estimating the two parameters of generalized logarithmic series distribution. These methods are the cuckoo search optimization, maximum likelihood estimation, and method of moments algorithms. All the required derivations and basic steps of each algorithm are explained. The applications for these algorithms are implemented through simulations using different sample sizes (n = 15, 25, 50, 100). Results are compared using the statistical measure mean square error.

Nonlinear stochastic exclusion financial dynamics modeling and complexity behaviors

In attempt to reproduce and investigate nonlinear dynamics of financial markets, a new random agent-based financial price dynamics is developed and investigated by stochastic exclusion process. The exclusion process, one of Markov interacting processes, is firstly introduced to imitate the trading interactions among the investing agents in this work and to explain various statistical facts found in financial data. To better understand the fluctuation complexity properties of the proposed model, the complex analyses of random logarithmic price return series are preformed, including power-law distribution, Lempel–Ziv complexity, correlation dimension analysis, maximum Lyapunov exponent, mean Lyapunov exponents and Kolmogorov–Sinai entropy density. In order to verify the rationality of the model, the corresponding analyses of real return series are also studied for comparison. The empirical research reveals that this financial model can reproduce similar statistical behaviors, power-law distribution of returns, complexity and chaotic features of returns for real stock markets.

On some aspects of a generalized alternative zero-inflated logarithmic series distribution

ABSTRACTHere, we consider a generalized form of the alternative zero-inflated logarithmic series distribution of Kumar and Riyaz (J. Statist. Comp. Simul., 2015) and study some of its important aspects. The parameters of the distribution are estimated by the method of maximum likelihood and some test procedures are developed for testing the significance of the additional parameter of the model. All these estimation and testing procedures are illustrated with the help of certain real life datasets. A simulation study is also carried out for assessing the performance of the estimators.

Investigating the Efficiency of the Indian Currency Market: A Persistence Perspective

The presence of long range persistence and its impact on policy decisions are examined in the Indian Forex market during the period between 2000 and 2015. Hurst-Mandelbrot's Classical R/S Statistic, Lo Statistic, Robinson's Estimate have been computed. Long memory in volatility and absolute return series of each currency pair were evidenced but the logarithmic return series of all these currency pairs indicate proclivity towards the “random walk” hypothesis. Therefore, currencies are not systematically over- or under-valued, which provides justification for passive index investment in these currencies. However, possibilities of speculation/hedging activities could not be ruled out which may call Reserve Bank’s intervention and interest smoothing behavior with potentials for impaired price discovery.

E-Bayesian Estimation of the Parameter of the Logarithmic Series Distribution

E-Bayesian estimation is introduced to estimate the parameter of logarithmic series distribution. In addition, E-Bayesian, Bayesian and maximum likelihood estimation with through applying mean squared error.

An order k version of the alternative zero-inflated logarithmic series distribution and its applications

ABSTRACT Here we introduce an order version of the alternative zero-inflated logarithmic series distribution of Kumar and Riyaz [14] and investigate some of its important properties by deriving an expression for its probability mass function, recurrence relations for its probabilities, raw moments and factorial moments. We discuss the estimation of the parameters of the distribution by the method of maximum likelihood. Certain test procedures are developed for testing the significance of the additional parameters of the model. All these procedures discussed in the paper are illustrated with the help of real life data sets. A simulation study is also considered for assessing the performance of the estimators.

Fourier coefficients of logarithmic vector-valued Poincaré series

We give an exact expression (Theorem 3.2) for the Fourier coefficients of logarithmic vector-valued Poincare series associated to representations where \(\rho (T)\) is a single Jordan block.

On the Bayes estimators of the parameters of size-biased generalized power series distributions

ABSTRACTIn this paper, we derive the Bayes estimators of functions of parameters of the size-biased generalized power series distribution under squared error loss function and weighted square error loss function. The results of size-biased GPSD are then used to obtain particular cases of the size-biased negative binomial, size-biased logarithmic series, and size-biased Poisson distributions. These estimators are better than the classical minimum variance unbiased estimators in the sense that they increase the range of the estimation. Finally, an example is provided to illustrate the results and a goodness of fit test is done using the maximum likelihood and Bayes estimators.

On accurately estimating stability thresholds for periodic spot patterns of reaction-diffusion systems in2

In the limit of an asymptotically large diffusivity ratio of order$\mathcal{O}$(ϵ−2) ≫ 1, steady-state spatially periodic patterns of localized spots, where the spots are centred at lattice points of a Bravais lattice, are well-known to exist for certain two-component reaction–diffusion systems (RD) in$\mathbb{R}$2. For the Schnakenberg RD model, such a localized periodic spot pattern is linearly unstable when the diffusivity ratio exceeds a certain critical threshold. However, since this critical threshold has an infinite-order logarithmic series in powers of the logarithmic gauge ν ≡ −1/log ϵ, a low-order truncation of this series is expected to be in rather poor agreement with the true stability threshold unless ϵ is very small. To overcome this difficulty, a hybrid asymptotic-numerical method is formulated and implemented that has the effect of summing this infinite-order logarithmic expansion for the stability threshold. The numerical implementation of this hybrid method relies critically on obtaining a rapidly converging infinite series representation of the regular part of the Bloch Green's function for the reduced-wave operator. Numerical results from the hybrid method for the stability threshold associated with a periodic spot pattern on a regular hexagonal lattice are compared with the two-term asymptotic results of [10] (Iron et al.J. Nonlinear Science, 2014). As expected, the difference between the two-term and hybrid results is rather large when ϵ is only moderately small. A related hybrid method is devised for accurately approximating the stability threshold associated with a periodic pattern of localized spots for the Gray-Scott RD system in$\mathbb{R}$2.

Non-global logarithms at finite N c beyond leading order

We analytically compute non-global logarithms at finite Nc fully up to 4 loops and partially at 5 loops, for the hemisphere mass distribution in e+e- to di-jets to leading logarithmic accuracy. Our method of calculation relies solely on integrating the eikonal squared-amplitudes for the emission of soft energy-ordered real-virtual gluons over the appropriate phase space. We show that the series of non-global logarithms in the said distribution exhibits a pattern of exponentiation thus confirming - by means of brute force - previous findings. In the large-Nc limit, our results coincide with those recently reported in literature. A comparison of our proposed exponential form with all-orders numerical solutions is performed and the phenomenological impact of the finite-Nc corrections is discussed.

A Modified Version of Logarithmic Series Distribution and Its Applications

In this article, we consider a modified version of logarithmic series distribution and study some of its properties. The maximum likelihood estimation of the parameters of the modified distribution is discussed and the distribution has been fitted to certain real life data sets. Tests are also carried out for justifying the significance of the additional parameter of the modified distribution.

Asymptotic expansions pertaining to the logarithmic series and related trigonometric sums

Asymptotic expansions pertaining to the logarithmic series and related trigonometric sums

Wideband Differentiator and Integrator With Ideal Phase Response

In this paper, we consider the design of a digital differentiator and integrator using the natural logarithm series. The proposed class of differentiators and integrators matches the ideal phase response and the magnitude response as closely as possible at low frequencies for orders lower than those reported in the literature. Furthermore, the bandwidth of the digital differentiator and integrator is extended to cover the entire Nyquist range using a simple multirate technique. In principle, the approach yields the results that are similar to those obtained by the design of fractional order differentiators and integrators.

A Discrete Analogue of Reciprocal Coordinate Subtangent and its Role in Characterization Problems

Abtsrcat The concept of reciprocal coordinate subtangent (RCST) has been used in statistical literature as a useful tool to study the monotone behaviours of a continuous density function and for characterizing probability distributions through its functional forms. Motivated by this, in the present paper, we consider a discrete analogue of RCST introduced by Gupta et al. (1997) and study its usefulness in modeling probability mass functions. Characterization results are proved for models viz. geometric, discrete Burr and modified power series. The concept is also extended to the weighted models and proves some useful results as models such as logarithmic series, residual lifetime and partial sum (renewal) distributions. Finally, a new definition for discrete analogue of RCST is introduced and examined its usefulness in modeling proportional hazard models in discrete time.

Type II Family of Bivariate Inflated-Parameter Generalized Power Series Distributions

The family of Inated-parameter Generalized Power Series distributions (IGPSD) was introduced by Minkova in 2002 as a compound Generalized Power Series distributions (GPSD) with geometric compounding distribution. In these notes we introduce a family of compound GPSDs with bivariate geometric compounding distribution. The probability mass function, recursion formulas, conditional distributions and some properties are given. A member of this family is a Type II bivariate Polya-Aeppli distribution, introduced by Minkova and Balakrishanan (2014). In this notes the particular cases of bivariate compound binomial, negative binomial and logarithmic series distributions are analyzed in detail.