scholarly journals Half Logistic Inverse Lomax Distribution with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 309
Author(s):  
Sanaa Al-Marzouki ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Parameters Estimation ◽  
Environmental Data ◽  
Stochastic Orders ◽  
Data Sets ◽  
Lomax Distribution ◽  
Derived Properties ◽  
Heavy Tailed ◽  
Inverse Lomax Distribution ◽  
Insurance Data ◽  
Methods Numerical

The last years have revealed the importance of the inverse Lomax distribution in the understanding of lifetime heavy-tailed phenomena. However, the inverse Lomax modeling capabilities have certain limits that researchers aim to overcome. These limits include a certain stiffness in the modulation of the peak and tail properties of the related probability density function. In this paper, a solution is given by using the functionalities of the half logistic family. We introduce a new three-parameter extended inverse Lomax distribution called the half logistic inverse Lomax distribution. We highlight its superiority over the inverse Lomax distribution through various theoretical and practical approaches. The derived properties include the stochastic orders, quantiles, moments, incomplete moments, entropy (Rényi and q) and order statistics. Then, an emphasis is put on the corresponding parametric model. The parameters estimation is performed by six well-established methods. Numerical results are presented to compare the performance of the obtained estimates. Also, a simulation study on the estimation of the Rényi entropy is proposed. Finally, we consider three practical data sets, one containing environmental data, another dealing with engineering data and the last containing insurance data, to show how the practitioner can take advantage of the new half logistic inverse Lomax model.

scholarly journals Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 601 ◽  
Author(s):  
Rashad A. R. Bantan ◽  
Mohammed Elgarhy ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Censored Data ◽  
Real Life ◽  
Data Sets ◽  
Lomax Distribution ◽  
Mean Squared Errors ◽  
True Value ◽  
Engineering Sciences ◽  
The Mean ◽  
Inverse Lomax Distribution ◽  
Applied Fields

The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

Seasonal variation of patulous Eustachian tube diagnoses using climatic and national health insurance data

2021 ◽  
pp. 1-7
Author(s):  
S Lee ◽  
S-W Choi ◽  
J Kim ◽  
H M Lee ◽  
S-J Oh ◽  
...  
Keyword(s):  
Relative Risk ◽  
Eustachian Tube ◽  
Climatic Factors ◽  
Data Sets ◽  
National Data ◽  
Health Insurance Data ◽  
Number Of Patients ◽  
Autumn And Winter ◽  
Insurance Data ◽  
Patulous Eustachian Tube

Abstract Objectives This study aimed to analyse if there were any associations between patulous Eustachian tube occurrence and climatic factors and seasonality. Methods The correlation between the monthly average number of patients diagnosed with patulous Eustachian tube and climatic factors in Seoul, Korea, from January 2010 to December 2016, was statistically analysed using national data sets. Results The relative risk for patulous Eustachian tube occurrence according to season was significantly higher in summer and autumn, and lower in winter than in spring (relative risk (95 per cent confidence interval): 1.334 (1.267–1.404), 1.219 (1.157–1.285) and 0.889 (0.840–0.941) for summer, autumn and winter, respectively). Temperature, atmospheric pressure and relative humidity had a moderate positive (r = 0.648), negative (r = –0.601) and positive (r = 0.492) correlation with the number of patulous Eustachian tube cases, respectively. Conclusion The number of patulous Eustachian tube cases was highest in summer and increased in proportion to changes in temperature and humidity, which could be due to physiological changes caused by climatic factors or diet trends.

Mixture copulas and insurance applications

2018 ◽  
Vol 12 (2) ◽  
pp. 391-411
Author(s):  
Maissa Tamraz
Keyword(s):  
Joint Distribution ◽  
Stable Distribution ◽  
Random Variable ◽  
Fixed Time ◽  
Collective Model ◽  
Data Sets ◽  
New Model ◽  
Time Period ◽  
Insurance Data ◽  
Dependence Property

AbstractIn the classical collective model over a fixed time period of two insurance portfolios, we are interested, in this contribution, in the models that relate to the joint distributionFof the largest claim amounts observed in both insurance portfolios. Specifically, we consider the tractable model where the claim counting random variableNfollows a discrete-stable distribution with parameters (α,λ). We investigate the dependence property ofFwith respect to both parametersαandλ. Furthermore, we present several applications of the new model to concrete insurance data sets and assess the fit of our new model with respect to other models already considered in some recent contributions. We can see that our model performs well with respect to most data sets.

scholarly journals An Environmental GIS-based Variable Analysis of SARS-CoV-2 in the City of Recife, Brazil

2020 ◽  
Author(s):  
Arthur Souza ◽  
Caroline Mota ◽  
Amanda Rosa ◽  
Ciro Figueiredo ◽  
Ana Lucia Candeias
Keyword(s):  
Low Income ◽  
Public Services ◽  
Spatial Regression ◽  
Case Fatality ◽  
Global Scale ◽  
Environmental Data ◽  
Data Sets ◽  
Spatial Regression Analysis ◽  
Effective Drugs ◽  
The City

Abstract Background: Given the increasing rates at which cases of people infected by Covid-19 have been evolving to case-fatality rates on a global scale and the context of there being a world-wide socio-economic crisis, decision-making must be undertaken based on prioritizing effective measures to control and combat the disease since there is a lack of effective drugs and as yet no vaccine. Method: This paper explores the determinant factors of the COVID-19 pandemic and its impacts on Recife, Pernambuco-Brazil by performing both local and global spatial regression analysis on two types of environmental data-sets. Data were obtained from ten specific days between late April and early July 2020, comprehending the ascending, peak and descending behaviours of the curve of infections.Results: This study highlights the importance of identifying and mapping clusters of the most affected neighbourhoods and their determinant effects. We have identified that it is increasingly common for there to be a phase in which hotspots of confirmed cases appear in a well-developed and heavily densely-populated neighbourhood of the city of Recife. From there, the disease is carried to areas characterised by having a precarious provision of public services and a low-income population and this quickly creates hotspots of case-fatality rates. The results also help to understand the influence of the age, income, level of education of the population and, additionally, of the extent to which they can access public services, on the behaviour of the virus across neighbourhoods.Conclusion: This study supports government measures against the spread of Covid-19 in heterogeneous cities, evidencing social inequality as a driver for a high incidence of fatal cases of the disease. Understanding the variables which influence the local dynamics of the virus spread becomes vital for identifying the most vulnerable regions for which prevention actions need to be developed.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

Recent Progress in Applying Advanced Computation Methods to Radar-Based Wave Measurements

2021 ◽  
Author(s):  
Morten Loell Vinther ◽  
Torbjørn Eide ◽  
Aurelia Paraschiv ◽  
Dickon Bonvik-Stone
Keyword(s):  
Doppler Radar ◽  
Risk Mitigation ◽  
Weather Conditions ◽  
Data Access ◽  
Environmental Data ◽  
Data Sets ◽  
Wave Measurements ◽  
Current Profiler ◽  
Pulse Doppler ◽  
Calm Weather

Abstract High quality environmental data are critical for any offshore activity relying on data insights to form appropriate planning and risk mitigation routines under challenging weather conditions. Such data are the most significant driver of future footprint reduction in offshore industries, in terms of costs savings, as well as operational safety and efficiency, enabled through ease of data access for all relevant stakeholders. This paper describes recent advancements in methods used by a dual-footprint Pulse-Doppler radar to provide accurate and reliable ocean wave height measurements. Achieved improvements during low wind weather conditions are presented and compared to data collected from other sources such as buoys and acoustic doppler wave and current profiler (ADCP) or legacy. The study is based on comparisons of recently developed algorithms applied to different data sets recorded at various sites, mostly covering calm weather conditions.

Mining Environmental Data in the ADMIRE Project Using New Advanced Methods and Tools

2012 ◽  
pp. 296-308
Author(s):  
Ondrej Habala ◽  
Martin Šeleng ◽  
Viet Tran ◽  
Branislav Šimo ◽  
Ladislav Hluchý
Keyword(s):  
Data Mining ◽  
Environmental Data ◽  
Environmental Applications ◽  
Data Sets ◽  
Distributed Data ◽  
New Methods ◽  
Prospective Application ◽  
Using Data ◽  
Computer Power

The project Advanced Data Mining and Integration Research for Europe (ADMIRE) is designing new methods and tools for comfortable mining and integration of large, distributed data sets. One of the prospective application domains for such methods and tools is the environmental applications domain, which often uses various data sets from different vendors where data mining is becoming increasingly popular and more computer power becomes available. The authors present a set of experimental environmental scenarios, and the application of ADMIRE technology in these scenarios. The scenarios try to predict meteorological and hydrological phenomena which currently cannot or are not predicted by using data mining of distributed data sets from several providers in Slovakia. The scenarios have been designed by environmental experts and apart from being used as the testing grounds for the ADMIRE technology; results are of particular interest to experts who have designed them.

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