Regional Flood Frequency Modeling for a Large Basin in India

The computation of flood magnitude and its likely occurrence to design different hydraulic structures are major challenges to the research community. The present study has been carried out to identify the homogeneous regions in the Mahanadi basin in Chhattisgarh part (data from 26 gauge/discharge sites) of India using conventional and clustering-based homogeneity tests and then computation and identification of probability weighted moment and L-moment based best regional distributions for different regions. Different simple to complex distributions like Extreme Value-I, Generalized Extreme Value, Logistic, Generalized Logistic, Generalized Pareto, Normal and Log-normal, Wakeby-4, and Wakeby-5 was used in the analysis through standardizing procedure to compute regional distributions. The best-fit distribution selected by simulating several series and compute L-kurtosis along with the L-moment ratio diagram. The homogeneity analysis confirmed that this basin can broadly be divided into two different homogeneous regions with 15 and 11 stations in the first (Region-1) and second (Region-2) regions respectively. The GEV distribution was found best suited for Region-1 while the Generalized Pareto worked well for Region-2. To make results more convenient for field application, catchment area-based equations were converted in the form of Dicken’s or Ryve’s formulae for these regions to estimate flood quantiles of any return period.

TOPP LEONE WEIBULL LOMAX DISTRIBUTION: PROPERTIES, REGRESSION MODEL AND APPLICATIONS

A new four-parameter lifetime distribution (called the Topp Leone Weibull-Lomax distribution) is proposed in this paper. Different mathematical properties of the proposed distribution were studied which include quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stochastic ordering, and stress-strength reliability parameter. The regression model and the residual analysis for the proposed model were also carried out. The model parameters were estimated by using the maximum likelihood criterion and the behaviour of these estimated parameters were examined by conducting a simulation study. The importance and flexibility of the proposed distribution have been proved empirically by using four separate data sets.

A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution

We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

Burr X Exponential – G Family of Distributions: Properties and Application

In this paper, we developed a new class of continuous distributions called Burr X Exponential-G Family. Also, we obtained sub-models of this family of distributions such as Burr X Exponential-Rayleigh (BXE-R) and Burr X Exponential Lomax (BXE-Lx) distributions; by showing their respective densities functions. Some structural properties of the proposed family of distributions were derived such as moment, moment generating function, probability weighted moment, renyi entropy and order statistics. We estimate the parameters of the model by using Maximum Likelihood methods. Finally, the results obtained are validated using two real data sets. The results show that BXE-Lx distribution provides better fit in the data sets than some other well known distributions. However, this new family of distributions will serve as an additional generator for developing new sub models to modeling positive real data sets.

Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton’s estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.