Rainfall modeling is significant for prediction and forecasting purposes in agriculture, weather derivatives, hydrology, and risk and disaster preparedness. Normally two models are used to model the rainfall process as a chain dependent process representing the occurrence and intensity of rainfall. Such two models help in understanding the physical features and dynamics of rainfall process. However rainfall data is zero inflated and exhibits overdispersion which is always underestimated by such models. In this study we have modeled the two processes simultaneously as a compound Poisson process. The rainfall events are modeled as a Poisson process while the intensity of each rainfall event is Gamma distributed. We minimize overdispersion by introducing the dispersion parameter in the model implemented through Tweedie distributions. Simulated rainfall data from the model shows a resemblance of the actual rainfall data in terms of seasonal variation, means, variance, and magnitude. The model also provides mechanisms for small but important properties of the rainfall process. The model developed can be used in forecasting and predicting rainfall amounts and occurrences which is important in weather derivatives, agriculture, hydrology, and prediction of drought and flood occurrences.

Nelson Christopher Dzupire

Philip Ngare

Leo Odongo

A Poisson-Gamma Model for Zero Inflated Rainfall Data

The circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series density estimator, has also been established. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics.

Yogendra P. Chaubey

Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

This study exploits the closure property of the converse convolution operator to come up with a hybrid Clayton-Frank Archimedean copula for two random variables. Pairs of random variables were generated and the upper tail observation of the cumulative distribution function (CDF) was used to assess the right skew behavior of the proposed model. Various values of the converse convolution operator were used to see their effect on the proposed model. The simulation covered lengths <span class="inline_break"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" width="17.789pt" style="vertical-align:-1.5765pt" id="M1" height="13.3506pt" version="1.1" viewBox="-0.0498162 -11.7741 17.789 13.3506"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-111" d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"/></g><g transform="matrix(.013,0,0,-0.013,10.158,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g></svg><span class="irelop"></span><svg xmlns:xlink="http://www.w3.org/1999/xlink" 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The proposed model was compared with about 40 other bivariate copulas (both Archimedean and elliptical). The proposed model had parameters that spanned the entire real line, thus removing restrictions on the parameters. The parameters theta and omega were varied for a selected interval and the hybrid Clayton-Frank model was, in most cases, found to outperform the other copulas under consideration.

Maxwell Akwasi Boateng

Akoto Yaw Omari-Sasu

Richard Kodzo Avuglah

Nana Kena Frempong

Hybrid Clayton-Frank Convolution-Based Bivariate Archimedean Copula

The estimation of the Smoothed Conditional Scale Function for time series was taken out under the conditional heteroscedastic innovations by imitating the kernel smoothing in nonparametric QAR-QARCH scheme. The estimation was taken out based on the quantile regression methodology proposed by Koenker and Bassett. And the proof of the asymptotic properties of the Conditional Scale Function estimator for this type of process was given and its consistency was shown.

Lema Logamou Seknewna

Peter Mwita Nyamuhanga

Benjamin Kyalo Muema

Smoothed Conditional Scale Function Estimation in AR(1)-ARCH(1) Processes

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

Masood Anwar

Jawaria Zahoor

The Half-Logistic Lomax Distribution for Lifetime Modeling

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher&#x2019;s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

Amna Bibi

The Half-Logistic Generalized Weibull Distribution

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Journal of Probability and Statistics