In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regression model. These applications showed empirically that the TRTG distribution outperforms some important discrete models such as the negative binomial, transmuted geometric, discrete Burr, discrete Chen, geometric, and Poisson distributions.

The estimation of stress-strength reliability $$R=P\left( X<Y\right) $$ R = P X < Y is a common problem in engineering and statistics. Traditional approaches typically rely on simple random sampling to estimate system reliability. In recent years, however, ranked set sampling has emerged as a cost-effective and efficient alternative to simple random sampling. Despite its growing popularity, the application of ranked set sampling to stress-strength reliability in discrete models remains underexplored in the literature. This paper addresses this gap by presenting a detailed statistical analysis of stress-strength reliability when stress and strength are modeled as independent discrete random variables having Poisson–Lindley distributions. We employ both point estimation and bootstrap confidence interval methods to derive stress-strength reliability estimates under both simple random sampling and ranked set sampling frameworks. To evaluate the effectiveness of these estimates, we conduct extensive Monte Carlo simulations, comparing their performance in different settings. The simulation results, complemented by analyses of two real datasets, show that ranked set sampling estimates generally outperform traditional simple random sampling estimates in terms of efficiency and accuracy. These results highlight the potential advantages of ranked set sampling in estimating system reliability and demonstrate the applicability of the method to discrete models, providing a valuable contribution to the field. The ranked set sampling method provides more consistent and reliable estimates compared to the simple random sampling method, with shorter confidence intervals and lower error rates, especially for small sample sizes.

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.

This article introduces a new lifetime distribution by merging the first two lower records based on exponential distribution and discusses the different features of the distribution. Statistical inferences about the distribution parameters are discussed with three estimation methods, namely maximum likelihood, least squares, and weighted least squares. Monte Carlo simulation study is performed to evaluate of these estimators based on mean square errors estimation, mean absolute deviation, and mean relative errors of estimation for a sample of different sizes. A distribution simulation analysis based on real data is provided to demonstrate the adaptability of the proposed model.

Özellik seçimi, veri analizinde veri hazırlamak için uygulanan ön işlemlerden biridir. Özellik seçimi basitçe orijinal özellik kümesinden en uygun özelliklerin alt kümesinin seçim işlemidir. Bu yöntemler, orijinal veri setinde alakasız ve gereksiz bilgiyi belirlemeye ve kaldırmaya çalışır. Bu çalışmada sınıf bilgisi kullanılarak değişim katsayısına dayalı yeni bir özellik seçim yöntemi önerilmiştir. Önerilen özellik seçim yönteminin etkinliği, gerçek veri setleri kullanılarak diğer iyi bilinen özellik seçim yöntemleri ile karşılaştırılarak değerlendirilmiştir. Özellik seçim yöntemlerinin performansı, karesel diskriminant analizinde sınıflama doğruluğu ve entropi kriterleri bakımından incelenmiştir. Çalışmada birim sayısının özellik sayısından fazla olduğu nicel verilerden oluşan üç gerçek veri seti kullanılmıştır. Her bir özellik seçim yöntemine göre önem sırası belirlenen özelliklerinden ilk d adet özellik kullanılarak karesel diskriminant analizi gerçekleştirilmiştir. Özellik sayısına göre özellik seçim yöntemlerinin karesel diskriminant analizindeki sınıflama doğruluğu ve entropi değerleri hesaplanmıştır. Çalışma sonuçları, önerilen özellik seçim yönteminin hesaplama basitliği ve etkinlik açısından sınıflama analizleri için iyi bilinen diğer özellik seçim yöntemleri karşısında güçlü bir alternatif olduğunu ortaya koymuştur.