Best fit probability distribution analysis of precipitation and potential evapotranspiration of India’s highly dense population state - Bihar

Planning of water resources and its management with the ambiguity and non-uniformity accompanying with precipitation and other meteorological physical characteristics may perhaps effect on agricultural production in Bihar where the farmers mostly depend on precipitation. The precipitation and potential evapotranspiration temporal distribution of the state is irregular due to geomorphology, climatic and other anthropogenic factors of the state. In the present study, attempt is taken to expose the best-fit probability distribution among the various available probability distribution of annual average precipitation and potential evapotranspiration based on 102 year of past records of all 37 districts of the state. On the basis of ranks of goodness of fit tests such as Kolmogorov Smirnov, Anderson Darling and Chi-Squared, the normal distribution was observed the best-fit probability distribution for 11 districts followed by Weibull (3P) for 9 districts, the Beta distribution for 5 districts and other distribution for rest districts for precipitation. Whereas Cauchy distribution was come out with the best-fit probability distribution for potential evapotranspiration for all districts and the second best was Gamma (3P) covering almost 60% of the total districts followed by General Extreme Value distribution (32%). The results can be used in future hydraulic design, hydrological study for estimation of return period and water resource planners for policy development.

An Asymmetric Bimodal Double Regression Model

In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented.

Analysis of the error distribution density convergence with its orthogonal decomposition in navigation measurements

Modern trends towards the expansion of online services lead to the need to determine the location of customers, who may also be on a moving object (vessel or aircraft, others vehicle – hereinafter the “Vehicle”). This task is of particular relevance in the fields of medicine – when organizing video conferencing for diagnosis and/or remote rehabilitation, e.g., for post-infarction and post-stroke patients using wireless devices, in education – when organizing distance learning and when taking exams online, etc. For the analysis of statistical materials of the accuracy of determining the location of a moving object, the Gaussian normal distribution is usually used. However, if the histogram of the sample has “heavier tails”, the determination of latitude and longitude’s error according to Gaussian function is not correct and requires an alternative approach. To describe the random errors of navigation measurements, mixed laws of a probability distribution of two types can be used: the first type is the generalized Cauchy distribution, the second type is the Pearson distribution, type VII. This paper has shown that it’s possible obtaining the decomposition of the error distribution density using orthogonal Hermite polynomials, without having its analytical expression. Our numerical results show that the approximation of the distribution function using the Gram-Charlier series of type A makes it possible to apply the orthogonal decomposition to describe the density of errors in navigation measurements. To compare the curves of density and its orthogonal decomposition, the density values were calculated. The research results showed that the normalized density and its orthogonal decomposition practically coincide.

Hilbert transform using a robust geostatistical method

In this paper, we introduced an efficient inversion method for Hilbert transform calculation which can be able to eliminate the outlier noise. The Most Frequent Value method (MFV) developed by Steiner merged with an inversion-based Fourier transform to introduce a powerful Fourier transform. The Fourier transform process (IRLS-FT) ability to noise overthrow efficiency and refusal to outliers make it an applicable method in the field of seismic data processing. In the first part of the study, we introduced the Hilbert transform stand on a efficient inversion, after that as an example we obtain the absolute value of the analytical signal which can be used as an attribute gauge. The method depends on a dual inversion, first we obtain the Fourier spectrum of the time signal via inversion, after that, the spectrum calculated via transformation of Hilbert transforms into time range using a efficient inversion. Steiner Weights is used later and calculated using the Iterative Reweighting Least Squares (IRLS) method (efficient inverse Fourier transform). Hermite functions in a series expansion are used to discretize the spectrum of the signal in time. These expansion coefficients are the unknowns in this case. The test procedure was made on a Ricker wavelet signal loaded with Cauchy distribution noise to test the new Hilbert transform. The method shows very good resistance to outlier noises better than the conventional (DFT) method.

Modified Group Method of Data Handling for Flood Quantile Prediction at Ungauged Site

Handling flood quantile with little data is essential in managing water resources. In this paper, we propose a potential model called Modified Group Method of Data Handling (MGMDH) to predict the flood quantile at ungauged sites in Malaysia. In this proposed MGMDH model, the principal component analysis (PCA) method is matched to the group method of data handling (GMDH) with various transfer functions. The MGMDH model consists of four transfer functions: polynomial, sigmoid, radial basis function, and hyperbolic tangent sigmoid transfer functions. The prediction performance of MGMDH models is compared to the conventional GMDH model. The appropriateness and effectiveness of the proposed models are demonstrated with a simulation study. Cauchy distribution is used in the simulation study as a disturbance error. The implementation of Cauchy Distribution as an error disturbance in artificial data illustrates the performance of the proposed models if the extreme value or extreme event occurs in the data set. The simulation study may say that the MGMDH model is superior to other comparison models, namely LR, NLR, GMDH and ANN models. Another beauty of this proposed model is that it shows a strong prediction performance when multicollinearity is absent in the data set.

Fuzzy Ensemble of Multi-Criteria Decision Making Methods for Heating Energy Transition in Danish Households

More than 110 countries, including 500 cities worldwide, have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. However, heating systems vary in energy source, heating technology, equipment location, and these complexities make it challenging for households to compare heating systems and make decisions. Hence, a decision support tool that provides a generalized ranking of individual heating alternatives is proposed for households as decision makers to identify the optimal choice. This paper presents an analysis of 13 heating alternatives and 19 quantitative criteria in technological, environmental, and financial aspects, combines ideal solution-based multi-criteria decision making with 6 weighting methods and 4 normalization methods, and introduces ensemble learning with a fuzzy membership function derived from Cauchy distribution to finalize the ultimate ranking. The robustness of the proposed method is verified by three sensitive analyses from different aspects. Air-to-water heat pump, solar heating and direct district heating are the top three rankings in the final result under Danish national average data. A framework is designed to guide decision makers to apply this ranking guideline with their practical, feasible situations.