Statistical Properties of Lomax-Inverse Exponential Distribution and Applications to Real Life Data

Abdulkadir, Sauta Saidu; Jerry, J.; Ieren, Terna Godfrey

doi:10.33003/fjs-2020-0402-435

Cited by 2 publications

(6 citation statements)

References 16 publications

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“…Mathematical expression for the order statistics is presented in this section. Suppose we have 𝑋 1 , 𝑋 2 , … , 𝑋 𝑛 as random sample of size 𝑛 from the Lomax Gumbel Type-two distribution with the CDF and PDF given as 𝐹(𝑥) 𝑎𝑛𝑑 𝑓(𝑥) respectively, let 𝑋 (1) , 𝑋 (2) , … , 𝑋 (𝑛) be the associated order statistics from the random variables in order of magnitude, then the probability density function of the order statistics 𝑋 (𝑠) of observation in the 𝑠 𝑡ℎ position is given by;…”

Section: Order Statisticsmentioning

confidence: 99%

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Lomax gamble type two distributions with applications to lifetime data

Adeyemi¹,

Adeleke²,

Akarawak³

2022

Int. J. Stat. Appl. Math.

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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.

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Section: Order Statisticsmentioning

confidence: 99%

“…Ijaz, Asim and Alamgir (2019) [11] introduced Lomax exponential distribution and Lomax inverse exponential by Abdulkadir, Jerry and leren (2020) [1] . The Gumbel Type-Two (GTT) distribution has received some further studies in literatures and some of the recent studies are presented in Table1.…”

Section: Introductionmentioning

confidence: 99%

Lomax gamble type two distributions with applications to lifetime data

Adeyemi¹,

Adeleke²,

Akarawak³

2022

Int. J. Stat. Appl. Math.

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“…By inserting Eq (7) into Eq (14), the CDF of the EGGIE distribution can be expressed as a linear combination of the IE distribution by…”

Section: Mixture Representationsmentioning

confidence: 99%

“… denote the exponential-G pdf with power parameter   1 l  . Therefore, by inserting Eq (7) and Eq (8) into Eq (19), we have the pdf of the EGGIE distribution given by…”

Section:  mentioning

confidence: 99%

“…Leren and Abdullahi [6] proposed the odd Lindley IE distribution with decreasing hazard rate function, some statistical properties, and two real datasets considered in demonstrating the practical importance of the distribution using the MLE procedure. Abdulkadir et al [7] proposed a two-parameter distribution called the Lomax IE distribution with derived properties such as the survival and hazard rate functions, quantile function, and order statistics. The MLE procedure utilizes fitting two sets of real datasets.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Modeling using A New Hybrid Form of The Inverted Exponential Distribution with Different Estimation Methods

Adubisi¹,

Adubisi

2022

InPrime:Ind.Jour.Pure.Applied.Math

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This paper introduces a new four-parameter distribution called the exponentiated Gompertz generated inverted exponential (EGGIE) distribution. Explicit expressions of the structural properties such as the ordinary and incomplete moments, probability weighted moments, quantile function, Lorenz and Bonferroni curves, entropies, and order statistics are derived. The empirical findings indicate that the maximum likelihood procedure dominates the other estimators in the simulation study while the Cramer-Von Mises procedure dominates in the two real datasets applications. We demonstrate the superiority of the EGGIE distribution over the Gompertz Lomax, odd Fréchet Inverse exponential, generalized inverse exponential, generalized inverse exponential, exponential inverse exponential, and Gompertz Weibull distribution using the maximum likelihood procedure utilizing two real datasets applications. The findings show that the EGGIE distribution yields the best goodness of fit to the two datasets.Keywords: exponentiated Gompertz generated family; inverse exponential distribution; Kolmogorov-Smirnov statistic; Anderson-Darling; maximum product spacing. AbstrakPaper ini memperkenalkan distribusi 4-parameter baru yang disebut dengan distribusi exponentiated Gompertz generated inverted exponential (EGGIE). Ekspresi eksplisit sifat struktural dari distribusi ini diturunkan, seperti momen biasa dan momen tak lengkap, momen probabilitas terboboti, fungsi kuartil, kurva Lorenz dan Bonferroni, entropi, dan statistik urutan. Temuan empiris menunjukan bahwa prosedur maksimum likelihood mendominasi estimator lainnya pada studi simulasi, sementara prosedur Cramer-Von Mises mendominasi pada aplikasi dua dataset nyata. Peneliti menunjukkan keunggulan dari distribusi EGGIE dibandingkan distribusi Gompertz Lomax, odd Frechet Inverse exponential, generalized inverse exponential, exponential inverse exponential, dan Gompertz Weibull menggunakan metode maksimum likelihood yang diaplikasikan pada dua dataset nyata. Hasil menunjukan bahwa distribusi EGGIE menghasilkan kecocokan model yang baik pada kedua dataset.Kata Kunci: keluarga bangkitan exponentiated Gompertz; distribusi inverse exponential; Kolmogorov-Smirnov statistic; Anderson-Darling; maximum product spacing. 2020MSC: 62E10

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Statistical Properties of Lomax-Inverse Exponential Distribution and Applications to Real Life Data

Cited by 2 publications

References 16 publications

Lomax gamble type two distributions with applications to lifetime data

Lomax gamble type two distributions with applications to lifetime data

Statistical Modeling using A New Hybrid Form of The Inverted Exponential Distribution with Different Estimation Methods

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