Kumaraswamy-Janardan Distribution: A Generalized Janardan Distribution with Application to Real Data

The quest to improve on flexibility of probability distributions motivated this research. Four-parameter Janardan generalized distribution known as Kumaraswamy-Janardan distribution is proposed through method of parameterization and studied. The probability density function, cumulative density function, survival rate function as well as hazard rate function of the distribution are established. Statistical properties such as moments, moment generating function as well as maximum likelihood of the model are discussed. The parameters are estimated using the simulated annealing optimization algorithm. Flexibility of the model in comparison with the baseline model as well as other competing sub-models is verified using Akaike Information Criteria (AIC). The model is tested with real data and is proven to be more flexible in fitting real data than any of its sub-models considered.

Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications

The authors introduce a new generalized distribution called the Marshall-Olkin Lindley-Log-logistic (MOLLLoG) distribution and discuss its distributional properties. The properties include hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Rényi entropy. A Monte Carlo simulation study was used to examine the bias, relative bias and mean square error of the maximum likelihood estimators. The betterness of the new distribution compared to other distributions is illustrated by means of two real life datasets.

The Transmuted Kumaraswamy Pareto Distribution

The generalization of probability distributions in view of improving their flexibility in capturing the shape and tail behavior of disparate data sets has become one of the most active aspects of statistical research. We developed a new Pareto distribution by using Kumaraswamy method which gave rise to a new distribution called Kumaraswamy Pareto distribution. This method is called transmutation. The mathematical properties of the new generalized distribution was presented using quartiles, moments, entropy, order statistics mean deviation and maximum likelihood method of parameter estimation. The new generalized distribution was applied to a real life data on the exceedances of flood peaks (in m3/s) where it was observed to be superior to its sub models in terms of some goodness-of-fit test such as log likelihood criterion, Akaike Information Criterion (AIC) and Kolmogorov-Smirnov (K-S) measures.

Case of Linagliptin-Induced Bullous Pemphigoid

Bullous pemphigoid is an autoimmune subepidermal blistering condition in which autoantibodies target components of the hemidesmosomal proteins. It typically presents as pruritic bullous lesions in a generalized distribution. Certain drugs such as diuretics, NSAIDs, antibiotics, and ACE inhibitors have been implicated in the development of bullous pemphigoid. Recently, a class of medications for type II diabetes, dipeptidyl peptidase-4 (DPP-4) inhibitors (commonly called gliptins) have been implicated in drug-induced bullous pemphigoid. We report a case of a 73-year-old female with type II diabetes mellitus who presented with biopsy-proven bullous pemphigoid after being treated with linagliptin. After discontinuing linagliptin and receiving first-line treatment, the patient achieved remission by her five-week follow-up. It is imperative that dermatologists and primary care physicians remain aware of this association when diagnosing and treating bullous pemphigoid, particularly in diabetic patients.

Climatic analysis of effective jet streams frequency on extreme precipitations in west of Iran

In this study, the frequency of effective jet streams was analyzed in extreme and widespread precipitations in the west of Iran. For this purpose, the daily precipitation of 69 synoptic and climatic stations over 18,624 days (1961–2010) were selected. Then, 119 days of extreme and widespread precipitation in the study area were chosen based on generalized distribution for conducting related reviews and analyses. The frequency of jet streams in the geographical location from 0° to 120°E and −10° to 80°N were reviewed at four levels (250, 300, 400 and 500 hPa). Due to the large volume of information, only the highest and lowest levels (250 and 500 hPa) in relation to the surface were considered. According to the results, the highest frequency of jet stream was observed at 250 hPa. The second quarter of the jet stream core lay over the west of Iran (which is associated with increasing positive vorticity as well as upper-level divergence and lower-level convergence of the atmosphere). In general, the extension of jet stream up to 500 hPa indicated an unstable layer thickness, which can cause extreme and widespread precipitation in the west of Iran. The results of selected days based on cluster analysis and Lund correlation revealed that in rainy days, the wind speed was more than 50 m/s and the subtropical jet stream speed was over 40 m/s, leading to extreme precipitation in the west of Iran.

The Weibull Logistic-exponential Distribution: Its Properties and Applications

In this paper, a new generalized distribution known as Weibull Logistic-Exponential Distribution (WLED) is proposed using the T-R{Y} framework. Several mathematical properties of this new distribution are studied. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit obtained by some comparable lifetime distributions.