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Journal articles on the topic 'Distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 June 2025

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1

Omer, Abdeen. "Medicines Distribution, Regulatory Privatisation, Social Welfare Services and Financing Alternatives." International Journal of Medical Reviews and Case Reports 2, Reports in Surgery and Dermatolo (2018): 1. http://dx.doi.org/10.5455/ijmrcr.medicine-distributions-sudan.

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2

Abdeen, Omer, Amiry Sabrina, and Inkov Ivan. "Medicines Distribution, Regulatory Privatisation, Social Welfare Services and Financing Alternatives." International Journal of Medical Reviews and Case Reports 3, no. 1 (July 2, 2018): 16–34. https://doi.org/10.5455/IJMRCR.medicine-distributions-sudan.

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The strategy of price liberalisation and privatisation had been implemented in Sudan over the last decade, and has had a positive result on government deficit. The investment law approved recently has good statements and rules on the above strategy in particular to pharmacy regulations. Under the pressure of the new privatisation policy, the government introduced radical changes in the pharmacy regulations. To improve the effectiveness of the public pharmacy, resources should be switched towards areas of need, reducing inequalities and promoting better health conditions. Medicines are financed either through cost sharing or full private. The role of the private services is significant. A review of reform of financing medicines in Sudan is given in this study. Also, it highlights the current drug supply system in the public sector, which is currently responsibility of the Central Medical Supplies Public Corporation (CMS). In Sudan, the researchers did not identify any rigorous evaluations or quantitative studies about the impact of drug regulations on the quality of medicines and how to protect public health against counterfeit or low quality medicines, although it is practically possible. However, the regulations must be continually evaluated to ensure the public health is protected against by marketing high quality medicines rather than commercial interests, and the drug companies are held accountable for their conduct.

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3

Panton, Don B. "Distribution function values for logstable distributions." Computers & Mathematics with Applications 25, no. 9 (May 1993): 17–24. http://dx.doi.org/10.1016/0898-1221(93)90128-i.

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4

Guo, Ran, and Jiulin Du. "Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?" Physica A: Statistical Mechanics and its Applications 406 (July 2014): 281–86. http://dx.doi.org/10.1016/j.physa.2014.03.056.

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5

Gómez, Héctor W., Osvaldo Venegas, and Heleno Bolfarine. "Skew-symmetric distributions generated by the distribution function of the normal distribution." Environmetrics 18, no. 4 (2007): 395–407. http://dx.doi.org/10.1002/env.817.

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6

C, Roshni, Venkatesan D, and B. Prasanth C. "A Generalized Area-Biased Power Ishita Distribution - Properties and Applications." Indian Journal of Science and Technology 17, no. 29 (July 30, 2024): 3037–43. https://doi.org/10.17485/IJST/v17i29.1515.

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Abstract <strong>Objectives:</strong> Generalized Area-Biased Power Ishita Distribution (GAPID) is a brand-new distribution that was suggested in this study. Its characterization is also mentioned in detail. <strong>Methods:</strong> The idea of weighted distributions is incorporated. This helps to derive new distributions that will be a best fit for many real-life data from many domains like agriculture, biomedical, financial, etc., where they may not match with the conventional distributions. Thus, it becomes necessary to create new distributions. The parameters have been calculated by maximum likelihood estimation. <strong>Findings:</strong> Its hazard rate function, survival function, and Moments, among other statistical features, were explored. <strong>Novelty:</strong> As results from classical distributions are insufficient for many Biomedical datasets, this novel distribution was fitted to a real data set of lung cancer patients' survival periods in months, allowing for a discussion of the data set's use. The superiority of the distribution is tested by comparing the same with known distributions and finding this one is better. Thereby the importance of the said distribution is established. <strong>Keywords:</strong> Estimate, Weighted distributions, Parameters, Reliability, Ishita distribution

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7

Maity, Mahuya, and Papiya Saha. "Normal Distribution." International Journal of Science and Research (IJSR) 12, no. 12 (December 5, 2023): 298–99. http://dx.doi.org/10.21275/sr231126211340.

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8

Chanda, Kiran. "Distribution Channels Used in Apple Distribution in Himachal Pradesh." International Journal of Scientific Engineering and Research 6, no. 9 (September 27, 2018): 32–36. https://doi.org/10.70729/ijser18179.

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9

Cousineau, Denis, Jean-Philippe Thivierge, Bradley Harding, and Yves Lacouture. "Constructing a group distribution from individual distributions." Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale 70, no. 3 (2016): 253–77. http://dx.doi.org/10.1037/cep0000069.

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10

Moya-Cessa, J. R., H. Moya-Cessa, L. R. Berriel-Valdos, O. Aguilar-Loreto, and P. Barberis-Blostein. "Unifying distribution functions: some lesser known distributions." Applied Optics 47, no. 22 (April 24, 2008): E13. http://dx.doi.org/10.1364/ao.47.000e13.

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11

Deshmukh, S. R., and M. S. Kasture. "BIVARIATE DISTRIBUTION WITH TRUNCATED POISSON MARGINAL DISTRIBUTIONS." Communications in Statistics - Theory and Methods 31, no. 4 (May 14, 2002): 527–34. http://dx.doi.org/10.1081/sta-120003132.

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12

Li, Kaican, and Zhi Geng. "The Noncentral Wishart Distribution and Related Distributions." Communications in Statistics - Theory and Methods 32, no. 1 (January 3, 2003): 33–45. http://dx.doi.org/10.1081/sta-120017798.

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13

Castillo, E., and J. Galambos. "Conditional distributions and the bivariate normal distribution." Metrika 36, no. 1 (December 1989): 209–14. http://dx.doi.org/10.1007/bf02614094.

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14

Voit, Eberhard O., and Shuiyang Yu. "The S-Distribution: Approximation of Discrete Distributions." Biometrical Journal 36, no. 2 (1994): 205–19. http://dx.doi.org/10.1002/bimj.4710360215.

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15

Çakmakyapan, Selen, and Gamze Özel Kadılar. "A New Customer Lifetime Duration Distribution: The Kumaraswamy Lindley Distribution." International Journal of Trade, Economics and Finance 5, no. 5 (October 2014): 441–44. http://dx.doi.org/10.7763/ijtef.2014.v5.412.

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16

C M, Latha, and Sandhya E. "CG and CEG Distributions with Uniform Secondary Distribution." International Journal of Scientific and Research Publications (IJSRP) 9, no. 12 (December 6, 2019): p9635. http://dx.doi.org/10.29322/ijsrp.9.12.2019.p9635.

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17

Dahel, S., and N. Giri. "Some distributions related to a noncentral wishart distribution." Communications in Statistics - Theory and Methods 23, no. 1 (January 1994): 229–37. http://dx.doi.org/10.1080/03610929408831249.

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18

Pudovkin, Alexander I., and Lutz Bornmann. "Approximation of citation distributions to the Poisson distribution." COLLNET Journal of Scientometrics and Information Management 12, no. 1 (January 2, 2018): 49–53. http://dx.doi.org/10.1080/09737766.2017.1332605.

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19

Nadarajah, Saralees, and Samuel Kotz. "Sampling distributions associated with the multivariate t distribution." Statistica Neerlandica 59, no. 2 (May 2005): 214–34. http://dx.doi.org/10.1111/j.1467-9574.2005.00288.x.

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20

Steliga, Katarzyna, and Dominik Szynal. "On counting distributions related to the Delaporte distribution." Applicationes Mathematicae 46, no. 1 (2019): 1–38. http://dx.doi.org/10.4064/am2337-8-2018.

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21

Tomaselli, Domenico, Paul Stursberg, Michael Metzger, and Florian Steinke. "Learning probability distributions over georeferenced distribution grid models." Electric Power Systems Research 235 (October 2024): 110636. http://dx.doi.org/10.1016/j.epsr.2024.110636.

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22

Schatzki, Thomas F. "Distribution of Aflatoxin in Pistachios. 1. Lot Distributions." Journal of Agricultural and Food Chemistry 43, no. 6 (June 1995): 1561–65. http://dx.doi.org/10.1021/jf00054a027.

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23

Boyd, Albert V. "Fitting the Truncated Pareto Distribution to Loss Distributions." Journal of the Staple Inn Actuarial Society 31 (March 1988): 151–58. http://dx.doi.org/10.1017/s2049929900010291.

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Hogg and Klugman use the truncated Pareto distribution with probability density functionwhere δ≥0 is specified and α > 0 and λ > 0 are unknown parameters, to describe insurance claims. This is fitted first of all by the method of moments, using the estimatorsand where is the mean of a simple random sample, and the (biased) varianceThe authors then suggest, on pp. 113–16, that these estimates be used as starting values in a Newton iteration to get the maximum likelihood estimates of the parameters, but this technique can fail as a result of convergence problems. The object of this note is to show that this has led Hogg and Klugman to underestimate seriously the area in the tail of a fitted loss distribution, and to discuss a method of circumventing this difficulty.

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24

Khmaladze, Estate. "Distribution free testing for conditional distributions given covariates." Statistics & Probability Letters 129 (October 2017): 348–54. http://dx.doi.org/10.1016/j.spl.2017.06.026.

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25

Liu, Tong, Ping Zhang, Wu-Sheng Dai, and Mi Xie. "An intermediate distribution between Gaussian and Cauchy distributions." Physica A: Statistical Mechanics and its Applications 391, no. 22 (November 2012): 5411–21. http://dx.doi.org/10.1016/j.physa.2012.06.035.

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26

Khmaladze, Estate. "Note on distribution free testing for discrete distributions." Annals of Statistics 41, no. 6 (December 2013): 2979–93. http://dx.doi.org/10.1214/13-aos1176.

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27

Newhall, Bruce, and Juan Arvelo. "Relating the distribution of bathymetry to clutter distributions." Journal of the Acoustical Society of America 118, no. 3 (September 2005): 2041. http://dx.doi.org/10.1121/1.4785846.

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28

Hady, Dina H. Abdel. "USE OF EXPONENTIAL DISTRIBUTION FOR HYBRIDIZATION OF DISTRIBUTIONS." Advances and Applications in Statistics 58, no. 1 (September 20, 2019): 57–75. http://dx.doi.org/10.17654/as058010057.

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29

Cirillo, Pasquale, Frank Redig, and Wioletta Ruszel. "Duality and stationary distributions of wealth distribution models." Journal of Physics A: Mathematical and Theoretical 47, no. 8 (February 10, 2014): 085203. http://dx.doi.org/10.1088/1751-8113/47/8/085203.

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30

Ahmadabadi, M. Nili, Y. Farjami, and M. B. Moghadam. "Approximating Distributions by Extended Generalized Lambda Distribution (XGLD)." Communications in Statistics - Simulation and Computation 41, no. 1 (January 2012): 1–23. http://dx.doi.org/10.1080/03610911003681503.

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31

Gharib, M. "Characterizations of the exponential distribution via mixing distributions." Microelectronics Reliability 36, no. 3 (March 1996): 293–305. http://dx.doi.org/10.1016/0026-2714(95)00131-x.

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32

Okubo, Tomoya, and Shin-ichi Mayekawa. "Approximating score distributions using mixed-multivariate beta distribution." Behaviormetrika 44, no. 2 (March 20, 2017): 369–84. http://dx.doi.org/10.1007/s41237-017-0019-7.

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33

Nguyen, T. T. "Conditional Distributions and Characterizations of Multivariate Stable Distribution." Journal of Multivariate Analysis 53, no. 2 (May 1995): 181–93. http://dx.doi.org/10.1006/jmva.1995.1031.

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34

Castro-Manzano, J. Martín. "Distribution Tableaux, Distribution Models." Axioms 9, no. 2 (April 17, 2020): 41. http://dx.doi.org/10.3390/axioms9020041.

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The concept of distribution is a concept within traditional logic that has been fundamental for the syntactic development of Sommers and Englebretsen’s term functor logic, a logic that recovers the term syntax of traditional logic. The issue here, however, is that the semantic counterpart of distribution for this logic is still in the making. Consequently, given this disparity between syntax and semantics, in this contribution we adapt some ideas of term functor logic tableaux to develop models of distribution, thus providing some alternative formal semantics to help close this breach.

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35

Sabir, Ali Siddiqui, Dwivedi Shradha, Alam Masood, Dwivedi Peeyush, Jain Sanjay, and Mustafa Ghulam. "MATHEMATICAL CHARACTERIZATION OF A NEW SIZE BIASED FAILURE DISTRIBUTION." Scientific Culture 10, no. 1 (May 14, 2024): 277–83. https://doi.org/10.5281/zenodo.11204699.

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The present study offers a mathematical study of a new size biased distributions which hasbeen developed for a failure distribution. Different important properties of the new distributionhave been obtained which includes mgf, CV, skewness, kurtosis and the distribution of orderstatistics.. The estimation of its parameter has been discussed using different methods.

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36

Rahmouni, Mohieddine, and Ayman Orabi. "The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution." International Journal of Statistics and Probability 7, no. 1 (November 2, 2017): 1. http://dx.doi.org/10.5539/ijsp.v7n1p1.

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This paper introduces a new two-parameter lifetime distribution, called the exponential-generalized truncated geometric (EGTG) distribution, by compounding the exponential with the generalized truncated geometric distributions. The new distribution involves two important known distributions, i.e., the exponential-geometric (Adamidis and Loukas, 1998) and the extended (complementary) exponential-geometric distributions (Adamidis et al., 2005; Louzada et al., 2011) in the minimum and maximum lifetime cases, respectively. General forms of the probability distribution, the survival and the failure rate functions as well as their properties are presented for some special cases. The application study is illustrated based on two real data sets.

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37

Ilori, Adetunji K., Omaku P. Enesi, Kole Emmanuel, Dayo V. Kayode, and Adebisi Michael. "Weighted Rayleigh Distribution." International Journal of Research and Innovation in Applied Science IX, no. VIII (2024): 323–36. http://dx.doi.org/10.51584/ijrias.2024.908030.

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This paper introduces the Weighted Rayleigh (WR) distribution by inducing inverted weight function into the existing Rayleigh distribution. Statistical and mathematical expressions of its properties such as Survival Function, Hazard Function, Moments, Moment Generating Function, Mean Deviation and Renyi entropy were explicitly derived. The model’s parameter was estimated using maximum likelihood method of estimation. Two real life data sets on cancer and waiting time before service were considered to assess the flexibility of the Weighted Rayleigh distribution over existing distributions. The distributions performance were compared using Log-likelihood and Akaike Information Criteria (AIC). The Weighted Rayleigh distribution fits the real life data better than the Rayleigh, Inverse Weibull (IW) and Weighted Inverse Weibull (WIW) distributions.

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38

Cao, Quang V., and Qinglin Wu. "Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution." Holzforschung 61, no. 2 (March 1, 2007): 124–30. http://dx.doi.org/10.1515/hf.2007.023.

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Abstract The length data from 12 samples of wood fibers and particles were described using lognormal and Weibull distributions. While both distributions fitted the middle range of the data well, the lognormal distribution provided a closer fit for short fibers and particles and the Weibull distribution was more appropriate for long ones. A mixture of the lognormal and Weibull distributions was developed using a variable weight to allow the new distribution to take the lognormal form for short fibers and gradually change to the Weibull form for long fibers. In the segmented distribution approach, a left segment of the lognormal distribution was joined to a right segment from the Weibull form. The Anderson-Darling goodness-of-fit test at the 5% level failed to reject the hypothesis that the mixture distribution and the segmented distribution fitted the data. Q-Q plots showed that both the mixture and segmented distributions provided an excellent fit to the fiber and particle length data, combining the best features of the lognormal and the Weibull distributions. These two new distributions are therefore better alternatives than the single lognormal and Weibull distributions for this data set.

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Osowole, Oyedeji Isola, Ngozi Nzelu, and Rita Nwaka. "Another Statistical Distribution: The Exponentiated Complementary Mukherjee-Islam Distribution." European Journal of Engineering and Technology Research 6, no. 1 (January 25, 2021): 118–23. http://dx.doi.org/10.24018/ejers.2021.6.1.2028.

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This study considered a newly proposed Exponentiated Complementary Mukherjee-Islam distribution obtained by exponentiating the Complementary Mukherjee-Islam distribution. Some properties of the new distribution were derived and results from the distribution indicated that the distribution is a better alternative than its baseline distribution. The new distribution is therefore a creditable addition to the existing family of exponentiated distributions.

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40

Osowole, Oyedeji Isola, Ngozi Nzelu, and Rita Nwaka. "Another Statistical Distribution: The Exponentiated Complementary Mukherjee-Islam Distribution." European Journal of Engineering and Technology Research 6, no. 1 (January 25, 2021): 118–23. http://dx.doi.org/10.24018/ejeng.2021.6.1.2028.

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This study considered a newly proposed Exponentiated Complementary Mukherjee-Islam distribution obtained by exponentiating the Complementary Mukherjee-Islam distribution. Some properties of the new distribution were derived and results from the distribution indicated that the distribution is a better alternative than its baseline distribution. The new distribution is therefore a creditable addition to the existing family of exponentiated distributions.

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41

Baranitharan, Balakrishnan, Karthik Chandran, Mathan Vaithilingam Subramaniyan, Subrata Chowdhury, Thi Thu Nguyen, and Duc-Tan Tran. "Probability distributions in Kerala's rainfall: implications for hydro energy planning." Probability distributions in Kerala's rainfall: implications for hydro energy planning 14, no. 3 (June 1, 2024): 3372–81. https://doi.org/10.11591/ijece.v14i3.pp3372-3381.

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Heavy rainfall has consistently acted as the primary catalyst for floods, resulting in numerous casualties and significant economic losses globally. Rainfall forecasting is accomplished by analysing existing rainfall data, which is then used to analyse the hydraulic system’s features. Gaining an understanding of rainfall requirements is a crucial challenge for every location, particularly in the case of India, given its diverse geographical area, population, and other influencing factors that impact various demands. This study evaluated the rainfall data for a span of 1990-2021 in six districts of Kerala State, India. To match the rainfall data from all districts, we utilized both Kaumarasamy-distribution and Dagum-distributions. Various Probabilistic tests, were employed to comparing these distributions. The results revealed that, in Kasargod, the Kumarasamy distribution demonstrates superior goodness-of-fit with the lowest Kolmogorov-Smirnov statistic (0.0597) and Anderson-darling statistic (2.271). However, in Wayanad, Malappuram, Palakkad, Idukki, and Trivandrum, the Dagum distribution consistently exhibits the most accurate fit, evident from its lowest Kolmogorov-Smirnov statistics (0.07447, 0.05435, 0.0556, 0.03636, 0.04291) and favourable Chi-Squared statistics (19.471, 8.4907, 19.239, 5.7318, 7.5297). These results emphasize the regional variation in precipitation data and the suitability of specific distribution models for accurate representation across different locations.

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42

VĂDUVA, Ion. "A PARTICULAR LIFETIME DISTRIBUTION." Review of the Air Force Academy 15, no. 2 (October 20, 2017): 5–14. http://dx.doi.org/10.19062/1842-9238.2017.15.2.1.

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43

Jawade, Sakshi Dinesh, and Dinesh V. Rojatkar. "Power Distribution - A Challange." International Journal of Trend in Scientific Research and Development Volume-1, Issue-6 (October 31, 2017): 790–93. http://dx.doi.org/10.31142/ijtsrd4657.

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44

Singh Kachhwaha, Jaideep. "COVID-19 Vaccine Distribution." International Journal of Science and Research (IJSR) 12, no. 2 (February 5, 2023): 254–55. http://dx.doi.org/10.21275/sr23202160226.

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45

Xaydarovich, Raimkulov Iskandar, Jabborov Giyosjon Gafforjonovich, Davlatov Ravshan Berdiyevich, and Xadjayeva Nigora Jurakulovna. "DISTRIBUTION OF CHICKEN ECTOPARASITES." American Journal of Veterinary Sciences and Wildlife Discovery 6, no. 3 (May 1, 2024): 17–20. http://dx.doi.org/10.37547/tajvswd/volume06issue03-04.

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This article presents literature data and results of preliminary research about ectoparasites that are widespread and cause great economic damage in chicken coops and some poultry farms. Their biology, distribution, clinical signs, epizootology and preventive measures are presented.

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46

Sam, Okemwa, Kiprono Kelvin, Eng. Peter Matuku DR., Eng. Clement Kiptum DR., and Eng. Emmanuel Kipkorir Prof. "SYNTHESIS: SMART RAINWATER HARVESTING, STORAGE AND DISTRIBUTION TO ENHANCE WATER SECURITY." International Journal of Civil and Structural Engineering Research 11, no. 1 (May 5, 2023): 32–37. https://doi.org/10.5281/zenodo.7898522.

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<strong>Abstract:</strong> This paper presents a novel approach to establish water security through autonomous rainwater harvesting, storage, and distribution mechanisms. The primary focus of the research is on developing a reliable and cost-effective method for harvesting, storing, and distributing rainwater in an autonomous manner, whereby the system is self-regulating in terms of harvesting, storing, and distributing water in response to localized and customized needs or conditions, more especially to communities that are struggling to meet their minimal water demands. The paper aims to develop an integrated and automated system that is capable of collecting, storing, and distributing rainwater in a sustainable manner, with the goal of increasing water security in areas with limited or unreliable water supply as exhibited in arid and semi-arid lands or places with poor water infrastructure conditions. The research will initially explore existing rainwater harvesting systems, including both conventional and innovative designs, in order to identify the most effective methods for harvesting rainwater. This will include looking at appropriate storage, filtration and distribution systems, as well as considering the economic, environmental, and social impacts of these systems, identifying the benefits and drawbacks of their system design deployment. Following this, the research will focus on developing an autonomous rainwater harvesting system that is capable of responding to economic, environmental and social factors in an efficient and cost-effective manner. This will involve the development of an integrated and automated system for collecting, storing and distributing rainwater, with an emphasis on sustainability and water security. The research will consider issues such as water scarcity, resource management, and environmental protection in order to ensure that the autonomous rainwater harvesting system is designed with these considerations in mind. Additionally, it will analyze the cost-effectiveness of the proposed system, and explore potential areas of application for the system. Finally, the paper will provide an assessment of the overall impact of the autonomous rainwater harvesting system on water security and consider the potential for further development and improvement of the system if sustainable. <strong>Keywords:</strong> rainwater harvesting, distribution mechanisms, distributing water, water security. <strong>Title:</strong> SYNTHESIS: SMART RAINWATER HARVESTING, STORAGE AND DISTRIBUTION TO ENHANCE WATER SECURITY <strong>Author:</strong> Sam Okemwa, Kelvin Kiprono, DR. Eng. Peter Matuku, DR. Eng. Clement Kiptum, Prof. Eng. Emmanuel Kipkorir <strong>International Journal of Civil and Structural Engineering Research   </strong> <strong>ISSN 2348-7607 (Online)</strong> <strong>Vol. 11, Issue 1, April 2023 - September 2023</strong> <strong>Page No: 32-37</strong> <strong>Research Publish Journals</strong> <strong>Website: www.researchpublish.com</strong> <strong>Published Date: 05-May-2023</strong> <strong>DOI: </strong><strong>https://doi.org/10.5281/zenodo.7898522</strong> <strong>Paper Download Link (Source)</strong> <strong>https://www.researchpublish.com/papers/synthesis-smart-rainwater-harvesting-storage-and-distribution-to-enhance-water-security</strong>

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47

Alzoubi, Loai, Ahmad Al-Khazaleh, Ayat Al-Meanazel, and Mohammed Gharaibeh. "EPANECHNIKOV-WEIBULL DISTRIBUTION." Journal of Southwest Jiaotong University 57, no. 6 (December 30, 2022): 949–58. http://dx.doi.org/10.35741/issn.0258-2724.57.6.81.

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The idea of using kernel functions combined with distributions to propose new distributions has recently been used to suggest new continuous distributions. This article combined the Epanechnikov kernel function with the Weibull distribution to produce the Epanechnikov-Weibull distribution (EWD). We have presented some properties of EWD, like the moments, MLEs, reliability analysis functions, Rényi entropy and the quantile function. We estimated the model parameters using the maximum likelihood method. A simulation study was conducted to calculate the MLE in terms of biases, mean square errors and mean relative, it shows that the estimates are consistent. Two real data set applications revealed that EWD is more flexible than the Weibull distribution.

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48

So, Jacky C. "The Distribution of Financial Ratios—A Note." Journal of Accounting, Auditing & Finance 9, no. 2 (April 1994): 215–23. http://dx.doi.org/10.1177/0148558x9400900205.

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Three competitive distributions are offered by the literature to explain the non-normality and skewness of the cross-sectional distribution of financial ratios: the mixture of normal distributions, the lognormal distribution, and the gamma distribution. Using a new technique, this paper shows that the lognormal distribution and the gamma distribution are not supported by the empirical evidence. Although these two distributions indeed capture skewness, they do not portray the correct shape of the distributions. The non-normal stable Paretian distribution seems to be good candidate to describe the distribution of financial ratios.

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49

Ch, V. Sastry. "Marshall-Olkin Stereographic Circular Logistic Distribution." YMER Digital 21, no. 06 (June 22, 2022): 664–68. http://dx.doi.org/10.37896/ymer21.06/66.

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Marshall and Olkin (1997) proposed an interesting method of adding a new parameter to the existing distributions. The resulting distributions are called the MarshallOlkin distributions, these distributions include the original distributions as a special case and are more flexible and represent a wide range of behavior than the original distributions. In this paper, a new class of asymmetric stereographic circular logistic distribution is introduced by using Marshall-Olkin transformation on stereographic circular logistic distribution (Dattatreyarao et al (2016)), named as Marshall-Olkin Stereographic Circular Logistic Distribution. The proposed model admits closed form density and distribution functions, generalizes the stereographic circular logistic model and is more flexible to model various types of data (symmetric and skew-symmetric circular data). Keywords:Characteristics, Stereographic circular logistic distribution, circular data, Marshall-Olkin transformation, l -axial data.

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GARCÍA, CATALINA BEATRIZ GARCÍA, JOSÉ GARCÍA PÉREZ, and SALVADOR CRUZ RAMBAUD. "THE GENERALIZED BIPARABOLIC DISTRIBUTION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17, no. 03 (June 2009): 377–96. http://dx.doi.org/10.1142/s0218488509005930.

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Abstract:

Beta distributions have been applied in a variety of fields in part due to its similarity to the normal distribution while allowing for a larger flexibility of skewness and kurtosis coverage when compared to the normal distribution. In spite of these advantages, the two-sided power (TSP) distribution was presented as an alternative to the beta distribution to address some of its short-comings, such as not possessing a cumulative density function (cdf) in a closed form and a difficulty with the interpretation of its parameters. The introduction of the biparabolic distribution and its generalization in this paper may be thought of in the same vein. Similar to the TSP distribution, the generalized biparabolic (GBP) distribution also possesses a closed form cdf, but contrary to the TSP distribution its density function is smooth at the mode. We shall demonstrate, using a moment ratio diagram comparison, that the GBP distribution provides for a larger flexibility in skewness and kurtosis coverage than the beta distribution when restricted to the unimodal domain. A detailed mean-variance comparison of GBP, beta and TSP distributions is presented in a Project Evaluation and Review Technique (PERT) context. Finally, we shall fit a GBP distribution to an example of financial European stock data and demonstrate a favorable fit of the GBP distribution compared to other distributions that have traditionally been used in that field, including the beta distribution.

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