A Doubling Technique for the Power Method Transformations

Power method polynomials are used for simulating non-normal distributions with specified product moments or L-moments. The power method is capable of producing distributions with extreme values of skew (L-skew) and kurtosis (L-kurtosis). However, these distributions can be extremely peaked and thus not representative of real-world data. To obviate this problem, two families of distributions are introduced based on a doubling technique with symmetric standard normal and logistic power method distributions. The primary focus of the methodology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivariate non-normal distributions with specified values of L-skew, L-kurtosis, and L-correlation. Evaluation of the proposed doubling technique indicates that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moments in terms of relative bias and relative efficiency when extreme non-normal distributions are of concern

An L-Moment Based Characterization of the Family of Dagum Distributions

This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of L-moments and L-correlation. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to their conventional product-moment based counterparts of skew, kurtosis, and Pearson correlation in terms of relative bias and relative efficiency–most notably in the context of heavy-tailed distributions

Uniform-based and triangular-based third-order power method distributions using a doubling technique distributions

Power method (PM) polynomials have been used for simulating non-normal distributions in a variety of settings such as toxicology research, price risk, business-cycle features, microarray analysis, computer adaptive testing, and structural equation modeling. A majority of the applications associated with the PM polynomials are based on the method of matching conventional moments (e.g., skew and kurtosis). However, estimators of skew and kurtosis can be (a) substantially biased, (b) highly dispersed, or (c) influenced by outliers. To address this limitation, two families of third-order PM distributions are developed through the method of -moments (Hosking, 1990) using a doubling technique (Morgenthaler & Tukey, 2000) and contrasted with the method of moments in the contexts of estimation of parameters. The methodology is based on simulating uniform- and triangular-based third-order PM distributions with specified values of -skew and - kurtosis. Monte Carlo simulation results indicate that the estimators based on method of Lmoments are superior to their conventional moment-based counterparts

Characterizing Tukey \u3ci\u3eh\u3c/i\u3e and \u3ci\u3ehh\u3c/i\u3e-Distributions through \u3ci\u3eL\u3c/i\u3e-Moments and the \u3ci\u3eL\u3c/i\u3e-Correlation

This paper introduces the Tukey family of symmetric h and asymmetric hh-distributions in the contexts of univariate L-moments and the L-correlation. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events (e.g., risk analysis, extreme events) and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy-tailed distributions are of concern

A Method for Simulating Burr Type III and Type XII Distributions through \u3ci\u3eL\u3c/i\u3e-Moments and \u3ci\u3eL\u3c/i\u3e-Correlations

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and the - correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of -skew, -kurtosis, and -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern

A Logistic \u3ci\u3eL\u3c/i\u3e-Moment-Based Analog for the Tukey \u3ci\u3eg-h, g, h\u3c/i\u3e, and \u3ci\u3eh-h\u3c/i\u3e System of Distributions

This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric γ-κ, (ii) log-logistic γ, (iii) symmetric κ, and (iv) asymmetric κL-κR. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavytailed distributions are of interest. A procedure is also described for simulating γ-κ, γ, κ, and κL-κR distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that estimates of L-skew, L-kurtosis, and L-correlation associated with the γ-κ, γ, κ, and κL-κR distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error

An \u3ci\u3eL\u3c/i\u3e-Moment-Based Analog for the Schmeiser-Deutsch Class of Distributions

This paper characterizes the conventional moment-based Schmeiser-Deutsch (S-D) class of distributions through the method of L-moments. The system can be used in a variety of settings such as simulation or modeling various processes. A procedure is also described for simulating S-D distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that the estimates of L-skew, L-kurtosis, and L-correlation associated with the S-D class of distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias—most notably when sample sizes are small

Performance of pilot-scale microbial fuel cells treating wastewater with associated bioenergy production in the Caribbean context

Microbial fuel cell (MFC) technology represents a form of renewable energy that generates bioelectricity from what would otherwise be considered a waste stream. MFCs may be ideally suited to the small island developing state (SIDS) context, such as Trinidad and Tobago where seawater as the main electrolyte is readily available and economical renewable and sustainable electricity is also deemed a priority. Hence this project tested two identical laboratory-scaled MFC systems that were specifically designed and developed for the Caribbean regional context. They consisted of two separate chambers, an anaerobic anodic chamber inoculated with wastewater and an aerobic cathodic chamber separated by a proton exchange membrane. Domestic wastewater from two various wastewater treatment plants inflow (after screening) was placed into the anodic chamber, and seawater from the Atlantic Ocean and Gulf of Paria placed into the cathodic chambers respectively with the bacteria present in the wastewater attaching to the anode. Experimental results demonstrated that the bacterial degradation of the wastewaters as substrate induced an electron flow through the electrodes producing bioelectricity whilst simultaneously reducing the organic matter as biochemical oxygen demand and chemical oxygen demand by 30 to 75%. The average bioenergy output for both systems was 84 mW/m² and 96 mW/m² respectively. This study demonstrated the potential for simultaneous bioenergy production and wastewater treatment in the SIDS context

An Improved Method for High Quality Metagenomics DNA Extraction from Human and Environmental Samples

To explore the natural microbial community of any ecosystems by high-resolution molecular approaches including next generation sequencing, it is extremely important to develop a sensitive and reproducible DNA extraction method that facilitate isolation of microbial DNA of sufficient purity and quantity from culturable and uncultured microbial species living in that environment. Proper lysis of heterogeneous community microbial cells without damaging their genomes is a major challenge. In this study, we have developed an improved method for extraction of community DNA from different environmental and human origin samples. We introduced a combination of physical, chemical and mechanical lysis methods for proper lysis of microbial inhabitants. The community microbial DNA was precipitated by using salt and organic solvent. Both the quality and quantity of isolated DNA was compared with the existing methodologies and the supremacy of our method was confirmed. Maximum recovery of genomic DNA in the absence of substantial amount of impurities made the method convenient for nucleic acid extraction. The nucleic acids obtained using this method are suitable for different downstream applications. This improved method has been named as the THSTI method to depict the Institute where the method was developed

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

Spinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signalto- noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far