Gumbel Type Research Articles

Joint modeling of correlated binary outcomes using multivariate logistic regression: contraception and HIV knowledge in Sri Lanka

Reproductive health significantly contributes to the overall well-being and social welfare of women. Within the spectrum of modern and traditional contraceptive methods in use, condoms have been strongly advocated by numerous HIV programs as a primary means of preventing HIV infection in Sri Lanka. Given the intrinsic relationship between contraceptive utilization and HIV awareness, our study aims to concurrently analyze the patterns of contraceptive usage and HIV knowledge, while accounting for their potential correlation. In this study, we introduced the application of the Gumbel type II distribution to effectively capture the interdependence of these joint probabilities, accounting for various covariates. The outcome of simulation studies demonstrated the superior performance of the integrated joint model, in comparison to the separate univariate models. Our findings highlighted several noteworthy risk factors associated with both contraceptive usage and HIV prevention knowledge. These included variables such as residence, level of education, wealth quintile, husband's education level, number of children, engagement with the newspapers, television viewership, and mobile phone usage. The Result indicates a positive association between the adoption of contraception and the awareness of HIV prevention measures, suggesting that individuals who actively embrace contraception are more likely to possess knowledge about preventing HIV transmission.

Statistical Modeling of Indus River Outflow at Tarbela Dam using Generalized Gumbel Type 2 Distribution

Statistical Modeling of Indus River Outflow at Tarbela Dam using Generalized Gumbel Type 2 Distribution

The strongest aftershock in seismic models of epidemic type

SUMMARY We consider an epidemic-type aftershock model, ETAS(F), for a large class of distributions F determining the number of direct aftershocks. This class includes Poisson, Geometric, Negative Binomial distributions and many other. Assuming an exponential form of the productivity and magnitude laws, we find a limiting distribution of the strongest aftershock magnitude μa when the initial cluster event m• is large. The regime can be either subcritical or critical; the initial event can be dominant in size or not. In the subcritical regime, the mode of the limiting distribution is determined by the parameters of productivity and the magnitude laws; the shape of this distribution is not universal and is effectively determined by F. For example, the Geometric F-distribution generates the logistic law, and the Poisson distribution (studied earlier) generates the Gumbel type 1 law. The accuracy of these laws for moderate initial magnitudes is tested numerically. The limit distribution of the Båth’s difference m• − μa is independent of the initial event size only if the regime is critical, and the ratio of exponents in the laws of magnitude and productivity is contained in the interval (1,2). Previous studies of the μa-distribution have dealt with the traditional Poisson F model and with arbitrary (not necessarily dominant) initial magnitude m•.

Power unit Gumbel type II distribution: Statistical properties, regression analysis, and applications

Using the power transformation method, we introduce a generalized version of the unit Gumbel type-2 distribution. The new lifetime distribution is called the power unit Gumbel type-2 distribution (PUGT2D). The new distribution’s statistical and reliability properties are given, and some estimation methods are proposed for estimating the model parameters. The usefulness and flexibility of the new distribution are illustrated with real datasets. Results based on log-likelihood, information statistics, and goodness-of-fit test results showed that the PUGT2D better fits the data than the other competing distributions. Moreover, a new regression model based on the new distribution is introduced and demonstrated to exhibit superior applicability through a numerical example.

Hydrological assessment of some old dams in Saudi Arabia under the current climate, environmental conditions, and the use of the advanced technology

Dams were built in Saudi Arabia (SA) starting from the late fifties. The rainfall record at that time is rather short since the early rainfall records in the study area were in the mid-sixties. Therefore, due to the recent changes in climatic conditions worldwide and having longer rainfall records nowadays, it is very important to assess the existing dams under the current conditions. The assessment is based on some criteria: the length of the rainfall records, the rainfall storm hyetographs, storm duration, the type of the rainfall frequency distribution, topographic data, and the current land use/land cover conditions. Fourteen dams in the Riyadh region are chosen, as a pilot study, to perform the proposed dam evaluation procedure. Later, the study can be extended to any region in SA. The results show that increasing the record length leads to a convergence of the rainfall to an asymptotic value. The minimum record length to produce stable statistical rainfall is about 20 years. Nine out of fourteen dams have a storage capacity less than the 5-year return period. The statistical analysis showed that the measured rainfall in some past years corresponds to 50 and 100 years return periods. Gumbel Type I distribution, which was used in the analysis of the old dams, does not seem to be the best distribution under the recent climate data. The dams should also be assessed under the effects of climate change and urban expansion.

Gumbel Type -2 Stress – Strength P(X<Y<Z) n-Cascade Reliability Estimation

In this paper, is derived the reliability of n-cascade stress-strength system model based on the Gumbel Type- 2 Distribution (GT-2) with unknown parameter λ and known parameters β , for probability of n- components having strengths Y between two stresses X and Z .In the Gumbel Type- 2 Distribution ,there are six methods of parameters and this system reliability estimators where discussed by using the Maximum Likelihood, Moments Method, Least Square Method, Weighted Least Square Method , Regression and Percentile ,based estimators on the simulation technique , these estimates are compared by the mean square error criteria for both small, medium and large samples .It has been concluded that the maximum likelihood estimator performs better than all the options considered.

THE SEROK RIVER CATCHMENT FLOOD HYDROGRAPH

Global climate change is expected to cause an increase in the intensity and duration of extreme rainfall events that occur today. The leading cause of flooding in various world regions, including flat coastal areas such as the Serok River catchment in Kota Pontianak, influenced by tides, is excessive rainfall. This article presents the results of an analysis of the impact of extreme precipitation on the peak discharge of flood hydrographs in the Serok River catchment, Kota Pontianak.Maximum daily rainfall data for 2009-2020 recorded at PTK-11 Pontianak Station were selected using the Annual Maximum Series Method. Frequency analysis was conducted using the best distribution method selected from Normal, Log Normal, Log Pearson Type III, and Gumbel Type I to obtain the design rainfall. The design rainfall was transformed into flood hydrographs at the next stage using the Snyder Synthetic Unit Hydrograph based on several return periods.The results of the analysis show that there are changes in flood discharge in the Serok River catchment area for each return period. The location of land use and the value of rain intensity significantly affect the calculation of plan discharge; the more significant the land area and the higher the rain intensity, the greater the resulting release. The most considerable flood discharge (Qmax) in the 2, 5, and 10 years return occurs at STA 1 + 100, w.290 m3/s, 0.347 m3/s, and 0.377 m3/s, respectively. Thus, this causes periodic flooding/inundation conditions, especially in areas that have low elevations.

Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model

Statistical models are vital in data analysis, and researchers are always on the search for potential or the latest statistical models to fit data sets in a variety of domains. To create an improved statistical model, we used a T-X transformation and the Gumbel Type-II model in this investigation. The research examined a simulation evaluation to assess the efficacy of the parameters. To show the application of the T-X approach for producing new distributions titled the new and improved Gumbel Type-II (NIGT-II) distribution, two actual data sets were used. The data sets reveal that the NIGT-II distribution sounds nicer than the Gumbel Type-II distribution.

The Reliability of Stored Water behind Dams Using the Multi-Component Stress-Strength System

Dams are essential infrastructure for managing water resources and providing entry to clean water for human needs. However, the construction and maintenance of dams require careful consideration of their reliability and safety, specifically in the event of extreme weather conditions such as heavy rainfall or flooding. In this study, the stress-strength model provides a useful framework for evaluating the reliability of dams and their ability to cope with external stresses such as water pressure, earthquake activity, and erosion. The Shasta reservoir in the United States is a prime example of a dam that requires regular assessment of its reliability to guarantee the safety of communities and infrastructure. The Gumbel Type II distribution has been suggested as a suitable model for fitting the collected data on the stress and strength of the reservoir behind the Shasta dam. Both classical and Bayesian approaches have been used to estimate the reliability function under the multi-component stress-strength model, and Monte Carlo simulation has been employed for parameter estimation. In addition, some measures of goodness-of-fit are employed to examine the suitability of the suggested model.

Sensitivity Analysis in Mean Annual Sediment Yield Modeling with Respect to Rainfall Probability Distribution Functions

An accurate estimation of the mean annual sediment yield from basins contributes to optimizing water resources planning and management. More specifically, both reservoir sedimentation and the damage caused to infrastructures fall within its field of application. Through a simple probabilistic combination function implemented in hydrometeorological models, this sediment yield can be estimated on a planning and management scale for ungauged basins. This probabilistic combination methodology requires the use of probability distribution functions to model design storms. Within these functions, SQRT-ET max and log-Pearson type III are currently highlighted in applied hydrology. Although the Gumbel distribution is also relevant, its use has progressively declined, as it has been considered to underestimate precipitation depth and flow discharge for high return periods, compared to the SQRT-ET max and log-Pearson III functions. The quantification of sediment yield through hydrometeorological models will ultimately be affected by the choice of the probability distribution function. The following four different functions were studied: Gumbel type I with a small sample size, Gumbel type I with a large sample size, log-Pearson type III and SQRT-ET max. To illustrate this, the model with these four functions has been applied in the Alto Palmones basin (South Iberian Peninsula). In this paper, it is shown that the application of Gumbel function type I with a small sample size, for the estimation of the mean annual sediment yield, provides values on the conservative side, with respect to the SQRT-ET max and log-Pearson type III functions.

Agrupamento Espacial da Precipitação Anual Extrema no Uruguai

Abstract The main objective of this work is to study the existence of spatial patterns maximum annual rainfall (through daily observations) within the territory of Uruguay and to show the application of two new statistical tools recently proposed. In the first stage, the distributions of maximum annual precipitation at each meteorological station will be studied. In the second stage, spatial clustering methods will be applied. To get the distribution of the maximum of each station, we have used a truncated Cramér-von Mises hypothesis test (the first statistical tool) and showed that it improves on the performance of the classic likelihood ratio test. It was found that in 18 study locations the distribution that best fits the data is of the Gumbel type, and for the other two, it is of the Fréchet type. Regarding the clustering methods, two methodologies were used, one of them was to perform clustering with the estimated parameters and the other was the PAM methodology using the F-madogram as distance, highlighting the homogeneity throughout the Uruguayan territory. Another novelty of this work (the second statistical tool) consists in including, as a complement to the clustering, the recently proposed independence test based on recurrence rates.

Matching of observations of dynamical systems, with applications to sequence matching

We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of Gumbel type that depends on both the length of the trajectories and on the Generalized Dimensions of the image measure. It is also modulated by an Extremal Index, that informs on the tendency of nearby observations to diverge along with the evolution of the dynamics. We give a formula for this quantity for a class of chaotic maps of the interval and regular observations. We present diverse numerical applications illustrating the theory and discuss the implications of these results for the study of physical systems. Finally, we discuss the connection between this problem and the problem of the longest matching block common to different sequences of symbols. In particular, we obtain a distributional result for strongly mixing processes.

SABER: A Model-Agnostic Postprocessor for Bias Correcting Discharge from Large Hydrologic Models

Hydrologic modeling is trending toward larger spatial and temporal domains, higher resolutions, and less extensive local calibration and validation. Thorough calibration and validation are difficult because the quantity of observations needed for such scales do not exist or is inaccessible to modelers. We present the Stream Analysis for Bias Estimation and Reduction (SABER) method for bias correction targeting large models. SABER is intended for model consumers to apply to a subset of a larger domain at gauged and ungauged locations and address issues with data size and availability. SABER extends frequency-matching postprocessing techniques using flow duration curves (FDC) at gauged subbasins to be applied at ungauged subbasins using clustering and spatial analysis. SABER uses a “scalar” FDC (SFDC), a ratio of simulated to observed FDC, to characterize biases spatially, temporally, and for varying exceedance probabilities to make corrections at ungauged subbasins. Biased flows at ungauged locations are corrected with the scalar values from the SFDC. Corrected flows are refined to fit a Gumbel Type 1 distribution. We present the theory, procedure, and validation study in Colombia. SABER reduces biases and improves composite metrics, including Nash Sutcliffe and Kling Gupta Efficiency. Recommendations for future work and a discussion of limitations are provided.

Asymptotic distribution of the maximum interpoint distance for high-dimensional data

Let X1,X2,…,Xn be a random sample coming from a p-dimensional population with independent sub-exponential components. Denote the maximum interpoint Euclidean distance by Mn=max1≤i<j≤n‖Xi−Xj‖. When the dimension p=p(n)→∞ with the sample size n→∞, it proves that Mn2 under a suitable normalization asymptotically obeys a Gumbel type distribution. The proofs mainly depend on the Stein–Chen Poisson approximation method and the moderate deviation of the sum of independent random variables.

Penanganan Banjir Sub-DAS Posindo Kota Balikpapan dengan Optimalisasi Penyediaan Infrastruktur Hijau

The Posindo sub-basin, emptying into the Ampal river, is experiencing floods, yet the city government has regularly normalized and cleaned the river. Therefore, this problem cannot be handled conventionally and generically. The research was conducted to formulate optimal flood management scenarios through a green infrastructure approach as an alternative for sustainable flood management. Two analytical methods were used to overcome the research question: the Gumbel Type I distribution to calculate rainfall return periods and HEC-HMS and HEC-RAS modeling software to simulate hydrological and hydraulic conditions. Result analysis showed an overflow discharge above the embankment along the Posindo sub-basin secondary channel by 0.38 – 1.64 m3/s. Alternative’s simulation shows that providing green open space (GOS) is crucial for maintaining water balance in the study area. The combined management scenario by maintaining a minimum GOS of 10%, storage ponds establishment, and increasing the drainage capacity adequate to reduce the overflow height.

Limiting Betti distributions of Hilbert schemes on n points

AbstractHausel and Rodriguez-Villegas (2015, Astérisque 370, 113–156) recently observed that work of Göttsche, combined with a classical result of Erdös and Lehner on integer partitions, implies that the limiting Betti distribution for the Hilbert schemes $(\mathbb {C}^{2})^{[n]}$ on $n$ points, as $n\rightarrow +\infty ,$ is a Gumbel distribution. In view of this example, they ask for further such Betti distributions. We answer this question for the quasihomogeneous Hilbert schemes $((\mathbb {C}^{2})^{[n]})^{T_{\alpha ,\beta }}$ that are cut out by torus actions. We prove that their limiting distributions are also of Gumbel type. To obtain this result, we combine work of Buryak, Feigin, and Nakajima on these Hilbert schemes with our generalization of the result of Erdös and Lehner, which gives the distribution of the number of parts in partitions that are multiples of a fixed integer $A\geq 2.$ Furthermore, if $p_{k}(A;n)$ denotes the number of partitions of $n$ with exactly $k$ parts that are multiples of $A$ , then we obtain the asymptotic $$ \begin{align*} p_{k}(A,n)\sim \frac{24^{\frac k2-\frac14}(n-Ak)^{\frac k2-\frac34}}{\sqrt2\left(1-\frac1A\right)^{\frac k2-\frac14}k!A^{k+\frac12}(2\pi)^{k}}e^{2\pi\sqrt{\frac1{6}\left(1-\frac1A\right)(n-Ak)}}, \end{align*} $$ a result which is of independent interest.

A novel extended Gumbel Type II model with statistical inference and Covid-19 applications

Statistical models play an important role in data analysis, and statisticians are constantly looking for new or relatively new statistical models to fit data sets across a wide range of fields. In this study, we used a new alpha power transformation and the Gumbel Type -II distribution to suggest an unique statistical model. The study contains a simulation analysis to determine the parameters’ efficiency. Two real-life data sets were utilized to demonstrate the use of novel alpha power Gumbel Type II (NAPGT-II) distribution. NAPGT-II distribution yields a better fit than Weibull, new alpha power exponential, exponentiated Gumbel Type-II, Gumbel Type-II and exponentiated generalized Gumbel Type-II distribution, as evidenced by the data.

Climate change-induced variations in future extreme precipitation intensity-duration-frequency in flood-prone city of Adama, central Ethiopia.

The influences of climate change on the features of extreme rainfall events have become unprecedented that needs improved understanding at all levels for planning effective management strategies of the potential risks. This study aims to assess the potential influences of climate change on extreme rainfall characteristics in flood-vulnerable city of Adama. Daily precipitation records of 1967-2016 and projection of global circulation models (GCMs): CanESM2 and HadCM3 for 2021-2070 were disaggregated into shorter time resolutions using the Hyetos model. Gumbel type I probability distribution and power-regression model ([Formula: see text] were used for deducing intensity-duration-frequency (IDF) curves and for describing their functions, respectively. The extreme rainfall intensity of the historical and future periods for a range of storm durations and return periods were compared and contrasted. A close agreement is obtained between the observed and the modeled rainfall intensity with high values of coefficient of determination (> 0.996) and Nash-Sutcliffe efficiency (> 0.850). Besides, statistically significant (p < 0.05) direct linear relationship is found between the return periods and the coefficient parameter of the IDF models. Moreover, the intensity of extreme precipitation over 2021-2070 in Adama city would increase up to 49.5%, depending on storm duration and return period considered. This could have consequences of the way the city's drainage infrastructures are designed, operated, and sustained. Hence, flood-prone areas should be recognized in order to formulate effective strategies for mitigation and adaption of potential impacts. The standards for designing future drainage infrastructures should also be updated aiming to reflect the effects of climatic change.

Simultaneous inference for autocovariances based on autoregressive sieve bootstrap

In this article, maximum deviations of sample autocovariances and autocorrelations from their theoretical counterparts over an increasing set of lags are considered. The asymptotic distribution of such statistics for physically dependent stationary time series, which is of Gumbel type, only depends on second‐order properties of the underlying time series. Since the autoregressive sieve bootstrap is able to mimic the second‐order structure asymptotically correctly it is an obvious problem whether the autoregressive (AR) sieve bootstrap, which has been shown to work for a number of relevant statistics in time series analysis, asymptotically works for maximum deviations of autocovariances and autocorrelations as well. This article shows that the question can be answered positively. Moreover, potential applications including spectral density estimation and an investigation of finite sample properties of the AR‐sieve bootstrap proposal by simulation are given.

A Comparative Study for Weighted Rayleigh Distribution

In this paper, Bayesian and non-Bayesian methods are used for parameter estimation of weighted Rayleigh (WR) distribution. Posterior distributions are derived under the assumption of informative and non-informative priors. The Bayes estimators and associated risks are obtained under different symmetric and asymmetric loss functions. Results are compared on the basis of posterior risk and mean square error using simulated and real life data sets. The study depicts that in order to estimate the scale parameter of the weighted Rayleigh distribution use of entropy loss function under Gumbel type II prior can be preferred. Also, Bayesian method of estimation having least values of mean squared error gives better results as compared to maximum likelihood method of estimation.