GERÇEK VERİ UYGULAMALARI VE MODEL KARŞILAŞTIRMALARI İLE İKİ YÖNLÜ GENELLEŞTİRİLMİŞ HİPERBOLİK SEKANT DAĞILIMI

Year 2021, Volume: 3 Issue: 2, 91 - 117, 31.12.2021

Mustafa Çağatay Korkmaz , Christophe Chesneau , Julien Marie

https://doi.org/10.51541/nicel.1015997

Abstract

Bu çalışmada, hiperbolik sekant dağılımının yeni bir versiyonunu elde etmek için standart iki yönlü kuvvet dağılım yapısı kullanılmıştır. Bu yeni dağılım, değerlerde ani bir değişiklik gösteren verilerin yorumlanması söz konusu olduğunda, hiperbolik sekant dağılımından daha esnektir. Makalenin ilk bölümünde, olasılık yoğunluğu ve tehlike oranı fonksiyonlarının biçim davranışı ve moment ölçümlerin analizi gibi bazı özelliklerine değinilmiştir. Sonrasında, baz alınan modelin istatistiksel yönü araştırılmıştır. Model parametreleri için en çok olabilirlik tahmin yönteminin yanı sıra bunları hesaplamak için kullanışlı bir algoritma sağlanmıştır. Tahminlerin ardından, önerilen modelleme stratejisinin potansiyelini göstermek için üç gerçek veri uygulaması sunulmuştur. Beta-normal, kuvvet-normal, Kuramaswamy-normal ve iki taraflı genelleştirilmiş normal dağılım modelleri rakip olarak kabul edilmiş olup, elde edilen sonuçların önerilen model için daha uygun olduğu görülmüştür.

TWO-SIDED GENERALIZED HYPERBOLIC SECANT DISTRIBUTION WITH REAL DATA APPLICATIONS AND MODEL COMPARISONS

Abstract

In this paper, we use the structure of the standard two-sided power distribution to implement a new version of the hyperbolic secant distribution. This new distribution is more flexible than the hyperbolic secant distribution when it comes to interpreting data presenting an abrupt change in values. In the first part of the paper, we show some of its properties, such as the shape behavior of the probability density and hazard rate functions, and the analysis of moment-type measures. Then, the statistical side of the underlying model is explored. We provide the maximum likelihood estimates for the model parameters, as well as an efficient algorithm to calculate them. After this, to demonstrate the potential of the proposed modeling strategy, we present three real data applications. The beta-normal, power-normal, Kuramaswamy-normal and two-sided generalized normal distribution models are considered as competitors. The results are favorable to the proposed model.

Keywords

Applications, General Family of Distribution, Model Comparisons, Standard Two-sided Power Distribution

References

• Chhikara, R. S. and Folks, J. L. (1977), The inverse gaussian distribution as a lifetime model, Technometrics, 9(4), 461-468.
• Cordeiro, G. and Castro, M. (2011), A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81, 883-898.
• Eugene, N., Lee, C. and Famoye, F. (2002), Beta-normal distribution and its application, Communications in Statistics-theory and Methods, 31, 497-512.
• Fischer, M. (2013), Generalized hyperbolic secant distributions: with Applications to Finance, Springer.
• Fischer, M. and Vaughan, D. (2002), Classes of skew generalized hyperbolic secant distributions, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics, Discussion Papers.
• Fischer, M. and Vaughan, D. (2004), The Beta-Hyperbolic secant (BHS) distribution, Friedrich-Alexander-UniversityErlangen-Nuremberg, Chair of Statistics and Econometrics, Discussion Papers, 39.
• Gilchrist, W. (2000), Statistical modelling with quantile functions, CRC Press, Abingdon.
• Gupta, R. C. and Gupta, R. D. (2008), Analyzing skewed data by power normal model, Test 17, 197- 210.
• Harkness, W. L. and Harkness, M. L. (1968), Generalized hyperbolic secant distributions, Journal of the American Statistical Association, 63(321), 329-337.
• Korkmaz, M. Ç. (2015), Two-sided generalized Gumbel distribution with application to air pollution data, International Journal of Statistical Distributions and Applications, 1, 19-26.
• Korkmaz, M. Ç. and Genç, A. İ. (2017), A new generalized two-sided class of distributions with an Emphasis on Two-sided Generalized Normal Distribution, Communications in Statistics - Simulation and Computation, doi: 10.1080/03610918.2015.1005233.
• Korkmaz, M. Ç. and Genç, A. İ. (2015b), Two-sided generalized exponential distribution, Communications in Statistics - Theory and Methods, 44(23), 5049-5070.
• Korkmaz, M. Ç. and Genç, A. İ. (2015a). A lifetime distribution based on a transformation of a two-sided power variate, Journal of Statistical Theory and Applications, 14(3), 265–280.
• Lee, E. T. and Wang, J. W. (2003), Statistical methods for survival data analysis, John Wiley & Sons, Inc.
• Morris, C. N. (1982), Natural exponential families with quadratic variance functions, The Annals of Statistics, 10(1), 65-80.
• Nasir, A., Jamal, F. and Chesneau, C. (2019), The odd generalized gamma-G family of distributions: Properties, regressions and applications. 2019. hal-01916828v4.
• Noor, I. and Mundher, K. (2020), Generalizations of Burr type X distribution with applications, ASM Science Journal. 1-8.
• Perez, J., Rambaud, S. and Garcia, C. (2005), The two-sided power distribution for the treatment of the uncertainty in PERT, Statistical Methods and Applications, 14, 209-222.
• Perks, W. F. (1932), On some experiments in the graduation of mortality statistics. Institute of Actuaries Journals, Series B, 58, 12-57.
• Reyes, J., Venegas, O. and G´omez G. H. (2017), Modified Slash Lindley distribution, Journal of Probability and Statistics.1-9.
• Van Dorp, J. R. and Kotz, S. (2002a), The standard two-sided power distribution and its properties: With applications in financial engineering. The American Statistician, 56, 90-99.
• Van Dorp, J. R. and Kotz, S. (2002b), A novel extension of the triangular distribution and its parameter estimation, The American Statistician, 51, 63-79.
• Vaughan, D. C. (2002). The generalized secant hyperbolic distribution and its properties, Communications in Statistics - Theory and Methods, 31(2), 219-238.