Lomax gamble type two distributions with applications to lifetime data

Abstract

The Gumbel Type-Two (GTT) distribution among many classical distributions has been found to lack the capacity to adequately fit some random phenomenon due to its monotonic failure rates thereby limiting its application. The Lomax-Generator was employed in this study to generalize the GTT distribution in order to derive the Lomax Gumbel Type-Two (LGTT) distribution capable of providing better modeling fits to real dataset. The new distribution has the Lomax Inverse Exponential distribution as a special case; the reliability and hazard rates functions were investigated. The distribution is unimodal, positively skewed and close to bell shape depending on parameter values. The quantile, median and order statistics were derived while the method of maximum likelihood estimation was used for estimating the parameters of the distribution. The proposed distribution demonstrated its potentials for modeling events whose distributions tends to be platykurtic, leptokurtic and approximately symmetric. Two lifetime survival datasets were analyzed using the distribution and results revealed the importance of application of LGTT distribution to the datasets with superior modeling fits than other four generalizations of GTT distributions existing in literatures derived using other generator. Three additional real life datasets were also used to compare the performance of LGTT with some distributions derived using Lomax as generator, results of analysis revealed that LGTT exhibits greater flexible potentials for modelling the real life datasets.

Enhanced Real-Life Data Modeling with the Modified Burr III Odds Ratio–G Distribution

“…Complex models, like the Burr III [5] and those related to the Weibull and exponential distributions, fail to model the bathtub-shaped dataset as well. These models include the Weibull generalized exponential distribution [26], the Type-2 Gumbel [27], the Lomax Gumbel Type-2 [28], and the Exponentiated Generalized Gumbel Type-2 distributions [29]. These observations further support the novelty and significance of the proposed model.…”

“…Given that the B-SIOR-E model derives from the Burr III and exponential distributions, we aim to benchmark it against other models based on Burr III [5], as well as those related to the Weibull and exponential distributions-Weibull generalized exponential (WGE) distribution [26], known for its applicability in complex scenarios. Furthermore, in light of Chen's work [25] on Type-2 Gumbel distributions, we have also incorporated comparisons with Type-2 Gumbel (T2G) [27], Lomax Gumbel Type-2 (LGT) [28], and Exponentiated Generalized Gumbel Type-2 (EGG2) distributions [29] into our analysis. It should be noted that both LGT and EGG2 have four parameters each.…”

The Lomax-Exponentiated Odds Ratio–G Distribution and Its Applications

“…In this section, we delve into applying our proposed model to datasets from the real world, aiming to illustrate its efficiency and flexibility. We test the Lomax-exponentiated odds ratio-exponential distribution (LEORE) against a selection of established models, including the exponentiated generalized Gumbel type-two (EGG2) [21], exponentiated Weibull logistic (EWL) [22], Lomax-Gumbel type-2 (LGT) [23], Kumaraswamy-Weibull (KW) [24], and type-2 Gumbel (T2G) [25].…”

Analysis of Students’ Creative Thinking Skills from the Perspective of Environmental Literacy and Digital Literacy Influence

“…In addition to the importance of developing environmental skills, it is also important to understand digital skills. In the era of the digital revolution, where information can be accessed anytime and anywhere through digital media [9][10][11], the use of digital media should align with its intended purposes: interaction and information retrieval. According to David Buckingham, digital media education aims to cultivate critical understanding and active participation when the use of digital media is misguided [12][13][14].…”