Mathematical and Computational Applications

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4 pages, 172 KiB

Open AccessEditorial

Preface to Computational Mathematics and Applied Statistics

by Sandra Ferreira

Math. Comput. Appl. 2023, 28(2), 31; https://doi.org/10.3390/mca28020031 - 27 Feb 2023

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Abstract

The rapid advances in modeling research have created new challenges and opportunities for statisticians [...] Full article

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Research

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17 pages, 2186 KiB

Open AccessArticle

The Binomial–Natural Discrete Lindley Distribution: Properties and Application to Count Data

by Shakaiba Shafiq, Sadaf Khan, Waleed Marzouk, Jiju Gillariose and Farrukh Jamal

Math. Comput. Appl. 2022, 27(4), 62; https://doi.org/10.3390/mca27040062 - 20 Jul 2022

Cited by 5 | Viewed by 2198

Abstract

In this paper, a new discrete distribution called Binomial–Natural Discrete Lindley distribution is proposed by compounding the binomial and natural discrete Lindley distributions. Some properties of the distribution are discussed including the moment-generating function, moments and hazard rate function. Estimation of the distribution’s [...] Read more.

In this paper, a new discrete distribution called Binomial–Natural Discrete Lindley distribution is proposed by compounding the binomial and natural discrete Lindley distributions. Some properties of the distribution are discussed including the moment-generating function, moments and hazard rate function. Estimation of the distribution’s parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square error. SO₂ data applications are also presented to see that the new distribution is useful in modeling data. Full article

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18 pages, 1976 KiB

Open AccessArticle

A Bivariate Beta from Gamma Ratios for Determining a Potential Variance Change Point: Inspired from a Process Control Scenario

by Schalk W. Human, Andriette Bekker, Johannes T. Ferreira and Philip Albert Mijburgh

Math. Comput. Appl. 2022, 27(4), 61; https://doi.org/10.3390/mca27040061 - 16 Jul 2022

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Abstract

Within statistical process control (SPC), normality is often assumed as the underlying probabilistic generator where the process variance is assumed equal for all rational subgroups. The parameters of the underlying process are usually assumed to be known—if this is not the case, some [...] Read more.

Within statistical process control (SPC), normality is often assumed as the underlying probabilistic generator where the process variance is assumed equal for all rational subgroups. The parameters of the underlying process are usually assumed to be known—if this is not the case, some challenges arise in the estimation of unknown parameters in the SPC environment especially in the case of few observations. This paper proposes a bivariate beta type distribution to guide the user in the detection of a permanent upward or downward step shift in the process’ variance that does not directly rely on parameter estimates, and as such presents itself as an attractive and intuitive approach for not only potentially identifying the magnitude of the shift, but also the position in time where this shift is most likely to occur. Certain statistical properties of this distribution are derived and simulation illustrates the theoretical results. In particular, some insights are gained by comparing the newly proposed model’s performance with an existing approach. A multivariate extension is described, and useful relationships between the derived model and other bivariate beta distributions are also included. Full article

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19 pages, 363 KiB

Open AccessArticle

Prony Method for Two-Generator Sparse Expansion Problem

by Abdulmtalb Hussen and Wenjie He

Math. Comput. Appl. 2022, 27(4), 60; https://doi.org/10.3390/mca27040060 - 15 Jul 2022

Cited by 3 | Viewed by 1746

Abstract

In data analysis and signal processing, the recovery of structured functions from the given sampling values is a fundamental problem. Many methods generalized from the Prony method have been developed to solve this problem; however, the current research mainly deals with the functions [...] Read more.

In data analysis and signal processing, the recovery of structured functions from the given sampling values is a fundamental problem. Many methods generalized from the Prony method have been developed to solve this problem; however, the current research mainly deals with the functions represented in sparse expansions using a single generating function. In this paper, we generalize the Prony method to solve the sparse expansion problem for two generating functions, so that more types of functions can be recovered by Prony-type methods. The two-generator sparse expansion problem has some special properties. For example, the two sets of frequencies need to be separated from the zeros of the Prony polynomial. We propose a two-stage least-square detection method to solve this problem effectively. Full article

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22 pages, 2815 KiB

Open AccessArticle

The Generalized Odd Linear Exponential Family of Distributions with Applications to Reliability Theory

by Farrukh Jamal, Laba Handique, Abdul Hadi N. Ahmed, Sadaf Khan, Shakaiba Shafiq and Waleed Marzouk

Math. Comput. Appl. 2022, 27(4), 55; https://doi.org/10.3390/mca27040055 - 23 Jun 2022

Cited by 5 | Viewed by 2674

Abstract

A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile function, moment generating function, distribution of [...] Read more.

A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile function, moment generating function, distribution of order statistics, moments, mean deviations, asymptotes and the stress–strength model of the proposed family are investigated. The maximum likelihood estimation of the parameters is presented. Simulation is carried out for two of the mentioned sub-models to check the asymptotic behavior of the maximum likelihood estimates. Two real-life data sets are used to establish the credibility of the proposed model. This is achieved by conducting data fitting of two of its sub-models and then comparing the results with suitable competitive lifetime models to generate conclusive evidence. Full article

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14 pages, 298 KiB

Open AccessArticle

A Note on Gerber–Shiu Function with Delayed Claim Reporting under Constant Force of Interest

by Kokou Essiomle and Franck Adekambi

Math. Comput. Appl. 2022, 27(3), 51; https://doi.org/10.3390/mca27030051 - 20 Jun 2022

Cited by 2 | Viewed by 1627

Abstract

In this paper, we analyze the Gerber–Shiu discounted penalty function for a constant interest rate in delayed claim reporting times. Using the Poisson claim arrival scenario, we derive the differential equation of the Laplace transform of the generalized Gerber–Shiu function and show that [...] Read more.

In this paper, we analyze the Gerber–Shiu discounted penalty function for a constant interest rate in delayed claim reporting times. Using the Poisson claim arrival scenario, we derive the differential equation of the Laplace transform of the generalized Gerber–Shiu function and show that the differential equation can be transformed to a Volterra equation of the second kind with a degenerated kernel. In the case of an exponential claim distribution, a closed-expression for the Gerber–Shiu function is obtained via sequence expansion. This result allows us to calculate the absolute (relative) ruin probability. Additionally, we discuss a method of solving the Volterra equation numerically and provide an illustration of the ruin’s probability to support the finding. Full article

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21 pages, 12344 KiB

Open AccessArticle

Morlet Cross-Wavelet Analysis of Climatic State Variables Expressed as a Function of Latitude, Longitude, and Time: New Light on Extreme Events

by Jean-Louis Pinault

Math. Comput. Appl. 2022, 27(3), 50; https://doi.org/10.3390/mca27030050 - 4 Jun 2022

Cited by 6 | Viewed by 2623

Abstract

This study aims to advance our knowledge in the genesis of extreme climatic events with the dual aim of improving forecasting methods while clarifying the role played by anthropogenic warming. Wavelet analysis is used to highlight the role of coherent Sea Surface Temperature [...] Read more.

This study aims to advance our knowledge in the genesis of extreme climatic events with the dual aim of improving forecasting methods while clarifying the role played by anthropogenic warming. Wavelet analysis is used to highlight the role of coherent Sea Surface Temperature (SST) anomalies produced from short-period oceanic Rossby waves resonantly forced, with two case studies: a Marine Heatwave (MHW) that occurred in the northwestern Pacific with a strong climatic impact in Japan, and an extreme flood event that occurred in Germany. Ocean–atmosphere interactions are evidenced by decomposing state variables into period bands within the cross-wavelet power spectra, namely SST, Sea Surface Height (SSH), and the zonal and meridional modulated geostrophic currents as well as precipitation height, i.e., the thickness of the layer of water produced during a day, with regard to subtropical cyclones. The bands are chosen according to the different harmonic modes of the oceanic Rossby waves. In each period band, the joint analysis of the amplitude and the phase of the state variables allow the estimation of the regionalized intensity of anomalies versus their time lag in relation to the date of occurrence of the extreme event. Regarding MHWs in the northwestern Pacific, it is shown how a warm SST anomaly associated with the northward component of the wind resulting from the low-pression system induces an SST response to latent and sensible heat transfer where the latitudinal SST gradient is steep. The SST anomaly is then shifted to the north as the phase becomes homogenized. As for subtropical cyclones, extreme events are the culmination of exceptional circumstances, some of which are foreseeable due to their relatively long maturation time. This is particularly the case of ocean–atmosphere interactions leading to the homogenization of the phase of SST anomalies that can potentially contribute to the supply of low-pressure systems. The same goes for the coalescence of distinct low-pressure systems during cyclogenesis. Some avenues are developed with the aim of better understanding how anthropogenic warming can modify certain key mechanisms in the evolution of those dynamic systems leading to extreme events. Full article

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16 pages, 758 KiB

Open AccessArticle

Small Area Estimation of Zone-Level Malnutrition among Children under Five in Ethiopia

by Kindie Fentahun Muchie, Anthony Kibira Wanjoya and Samuel Musili Mwalili

Math. Comput. Appl. 2022, 27(3), 44; https://doi.org/10.3390/mca27030044 - 22 May 2022

Cited by 1 | Viewed by 3127

Abstract

Child undernutrition is one of the 10 most significant public health problems worldwide. There is a rapidly growing demand to produce reliable estimates at the micro administrative level with small sample sizes. In this research, the authors employed small area estimation techniques to [...] Read more.

Child undernutrition is one of the 10 most significant public health problems worldwide. There is a rapidly growing demand to produce reliable estimates at the micro administrative level with small sample sizes. In this research, the authors employed small area estimation techniques to estimate the prevalence of malnutrition at the zonal level among children under five in Ethiopia. The small area estimation concept was sought for by linking the most recent possible survey data and census data in Ethiopia. The results show that there is spatial variation of stunting, wasting and being underweight across the zone level, showing different locations facing different challenges or different extents. Full article

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16 pages, 444 KiB

Open AccessArticle

Applications of the Sine Modified Lindley Distribution to Biomedical Data

by Lishamol Tomy, Veena G and Christophe Chesneau

Math. Comput. Appl. 2022, 27(3), 43; https://doi.org/10.3390/mca27030043 - 16 May 2022

Cited by 3 | Viewed by 2273

Abstract

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth [...] Read more.

In this paper, the applicability of the sine modified Lindley distribution, recently introduced in the statistical literature, is highlighted via the goodness-of-fit approach on biological data. In particular, it is shown to be beneficial in estimating and modeling the life periods of growth hormone guinea pigs given tubercle bacilli, growth hormone treatment for children, and the size of tumors in cancer patients. We anticipate that our model will be effective in modeling the survival times of diseases related to cancer. The R codes for the figures, as well as information on how the data are processed, are provided. Full article

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17 pages, 4595 KiB

Open AccessArticle

Multivariable Panel Data Cluster Analysis of Meteorological Stations in Thailand for ENSO Phenomenon

by Porntip Dechpichai, Nuttawadee Jinapang, Pariyakorn Yamphli, Sakulrat Polamnuay, Sittisak Injan and Usa Humphries

Math. Comput. Appl. 2022, 27(3), 37; https://doi.org/10.3390/mca27030037 - 24 Apr 2022

Cited by 3 | Viewed by 2576

Abstract

The purpose of this research is to study the spatial and temporal groupings of 124 meteorological stations in Thailand under ENSO. The multivariate climate variables are rainfall, relative humidity, temperature, max temperature, min temperature, solar downwelling, and horizontal wind from the conformal cubic [...] Read more.

The purpose of this research is to study the spatial and temporal groupings of 124 meteorological stations in Thailand under ENSO. The multivariate climate variables are rainfall, relative humidity, temperature, max temperature, min temperature, solar downwelling, and horizontal wind from the conformal cubic atmospheric model (CCAM) in years of El Niño (1987, 2004, and 2015) and La Niña (1999, 2000, and 2011). Euclidean distance timed and spaced with average linkage for clustering and silhouette width for cluster validation were employed. Five spatial clusters (SCs) and three temporal clusters (TCs) in each SC with different average precipitation were compared by El Niño and La Niña. The pattern of SCs and TCs was similar for both events except in the case when severe El Niño occurred. This method could be applied using variables forecasted in the future to be used for planning and managing crop cultivation with the climate change in each area. Full article

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14 pages, 2177 KiB

Open AccessArticle

On the Prediction of Evaporation in Arid Climate Using Machine Learning Model

by Mansura Jasmine, Abdolmajid Mohammadian and Hossein Bonakdari

Math. Comput. Appl. 2022, 27(2), 32; https://doi.org/10.3390/mca27020032 - 5 Apr 2022

Cited by 6 | Viewed by 2678

Abstract

Evaporation calculations are important for the proper management of hydrological resources, such as reservoirs, lakes, and rivers. Data-driven approaches, such as adaptive neuro fuzzy inference, are getting popular in many hydrological fields. This paper investigates the effective implementation of artificial intelligence on the [...] Read more.

Evaporation calculations are important for the proper management of hydrological resources, such as reservoirs, lakes, and rivers. Data-driven approaches, such as adaptive neuro fuzzy inference, are getting popular in many hydrological fields. This paper investigates the effective implementation of artificial intelligence on the prediction of evaporation for agricultural area. In particular, it presents the adaptive neuro fuzzy inference system (ANFIS) and hybridization of ANFIS with three optimizers, which include the genetic algorithm (GA), firefly algorithm (FFA), and particle swarm optimizer (PSO). Six different measured weather variables are taken for the proposed modelling approach, including the maximum, minimum, and average air temperature, sunshine hours, wind speed, and relative humidity of a given location. Models are separately calibrated with a total of 86 data points over an eight-year period, from 2010 to 2017, at the specified station, located in Arizona, United States of America. Farming lands and humid climates are the reason for choosing this location. Ten statistical indices are calculated to find the best fit model. Comparisons shows that ANFIS and ANFIS–PSO are slightly better than ANFIS–FFA and ANFIS–GA. Though the hybrid ANFIS–PSO (

R^{2} =

0.99, VAF = 98.85, RMSE = 9.73, SI = 0.05) is very close to the ANFIS (

R^{2}

= 0.99, VAF = 99.04, RMSE = 8.92, SI = 0.05) model, preference can be given to ANFIS, due to its simplicity and easy operation. Full article

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13 pages, 1670 KiB

Open AccessArticle

Nadarajah–Haghighi Lomax Distribution and Its Applications

by Vasili B. V. Nagarjuna, Rudravaram Vishnu Vardhan and Christophe Chesneau

Math. Comput. Appl. 2022, 27(2), 30; https://doi.org/10.3390/mca27020030 - 1 Apr 2022

Cited by 5 | Viewed by 3627

Abstract

Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made [...] Read more.

Over the years, several researchers have worked to model phenomena in which the distribution of data presents more or less heavy tails. With this aim, several generalizations or extensions of the Lomax distribution have been proposed. In this paper, an attempt is made to create a hybrid distribution mixing the functionalities of the Nadarajah–Haghighi and Lomax distributions, namely the Nadarajah–Haghighi Lomax (NHLx) distribution. It can also be thought of as an extension of the exponential Lomax distribution. The NHLx distribution has the features of having four parameters, a lower bounded support, and very flexible distributional functions, including a decreasing or unimodal probability density function and an increasing, decreasing, or upside-down bathtub hazard rate function. In addition, it benefits from the treatable statistical properties of moments and quantiles. The statistical applicability of the NHLx model is highlighted, with simulations carried out. Four real data sets are also used to illustrate the practical applications. In particular, results are compared with Lomax-based models of importance, such as the Lomax, Weibull Lomax, and exponential Lomax models, and it is observed that the NHLx model fits better. Full article

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19 pages, 4512 KiB

Open AccessArticle

The Minimum Lindley Lomax Distribution: Properties and Applications

by Sadaf Khan, Gholamhossein G. Hamedani, Hesham Mohamed Reyad, Farrukh Jamal, Shakaiba Shafiq and Soha Othman

Math. Comput. Appl. 2022, 27(1), 16; https://doi.org/10.3390/mca27010016 - 18 Feb 2022

Cited by 3 | Viewed by 2500

Abstract

By fusing the Lindley and Lomax distributions, we present a unique three-parameter continuous model titled the minimum Lindley Lomax distribution. The quantile function, ordinary and incomplete moments, moment generating function, Lorenz and Bonferroni curves, order statistics, Rényi entropy, stress strength model, and stochastic [...] Read more.

By fusing the Lindley and Lomax distributions, we present a unique three-parameter continuous model titled the minimum Lindley Lomax distribution. The quantile function, ordinary and incomplete moments, moment generating function, Lorenz and Bonferroni curves, order statistics, Rényi entropy, stress strength model, and stochastic sequencing are all carefully examined as basic statistical aspects of the new distribution. The characterizations of the new model are investigated. The proposed distribution’s parameters were evaluated using the maximum likelihood procedures. The stability of the parameter estimations is explored using a Monte Carlo simulation. Two applications are used to objectively assess the new model’s extensibility. Full article

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20 pages, 1505 KiB

Open AccessArticle

The Unit Teissier Distribution and Its Applications

by Anuresha Krishna, Radhakumari Maya, Christophe Chesneau and Muhammed Rasheed Irshad

Math. Comput. Appl. 2022, 27(1), 12; https://doi.org/10.3390/mca27010012 - 1 Feb 2022

Cited by 17 | Viewed by 3360

Abstract

A bounded form of the Teissier distribution, namely the unit Teissier distribution, is introduced. It is subjected to a thorough examination of its important properties, including shape analysis of the main functions, analytical expression for moments based on upper incomplete gamma function, incomplete [...] Read more.

A bounded form of the Teissier distribution, namely the unit Teissier distribution, is introduced. It is subjected to a thorough examination of its important properties, including shape analysis of the main functions, analytical expression for moments based on upper incomplete gamma function, incomplete moments, probability-weighted moments, and quantile function. The uncertainty measures Shannon entropy and extropy are also performed. The maximum likelihood estimation, least square estimation, weighted least square estimation, and Bayesian estimation methods are used to estimate the parameters of the model, and their respective performances are assessed via a simulation study. Finally, the competency of the proposed model is illustrated by using two data sets from diverse fields. Full article

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17 pages, 393 KiB

Open AccessArticle

New Modified Burr III Distribution, Properties and Applications

by Farrukh Jamal, Ali H. Abuzaid, Muhammad H. Tahir, Muhammad Arslan Nasir, Sadaf Khan and Wali Khan Mashwani

Math. Comput. Appl. 2021, 26(4), 82; https://doi.org/10.3390/mca26040082 - 20 Dec 2021

Cited by 3 | Viewed by 3420

Abstract

In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate function including increasing, decreasing, bathtub, upside-down bathtub, and [...] Read more.

In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate function including increasing, decreasing, bathtub, upside-down bathtub, and nearly constant. Some of its elementary properties, such as rth moments, sth incomplete moments, moment generating function, skewness, kurtosis, mode, ith order statistics, and stochastic ordering, are presented in a clear and concise manner. The well-established technique of maximum likelihood is employed to estimate model parameters. Middle-censoring is considered as a modern general scheme of censoring. The efficacy of the proposed model is asserted through three applications consisting of complete and censored samples. Full article

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15 pages, 468 KiB

Open AccessArticle

The Sine Modified Lindley Distribution

by Lishamol Tomy, Veena G and Christophe Chesneau

Math. Comput. Appl. 2021, 26(4), 81; https://doi.org/10.3390/mca26040081 - 16 Dec 2021

Cited by 5 | Viewed by 2413

Abstract

The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. [...] Read more.

The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance. Full article

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22 pages, 478 KiB

Open AccessArticle

Discrete Pseudo Lindley Distribution: Properties, Estimation and Application on INAR(1) Process

by Muhammed Rasheed Irshad, Christophe Chesneau, Veena D’cruz and Radhakumari Maya

Math. Comput. Appl. 2021, 26(4), 76; https://doi.org/10.3390/mca26040076 - 12 Nov 2021

Cited by 9 | Viewed by 2853

Abstract

In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and [...] Read more.

In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and stress–strength reliability made the distribution favourable. Two different methods are considered for the estimation of unknown parameters and, hence, compared with a broad simulation study. The practicality of the proposed distribution is illustrated in the first-order integer-valued autoregressive process. Its empirical importance is proved through three real datasets. Full article

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31 pages, 745 KiB

Open AccessReview

Statistical Techniques for Environmental Sciences: A Review

by Lishamol Tomy, Christophe Chesneau and Amritha K. Madhav

Math. Comput. Appl. 2021, 26(4), 74; https://doi.org/10.3390/mca26040074 - 4 Nov 2021

Cited by 5 | Viewed by 12074

Abstract

This paper reviews the interdisciplinary collaboration between Environmental Sciences and Statistics. The usage of statistical methods as a problem-solving tool for handling environmental problems is the key element of this approach. This paper enhances a clear pavement for environmental scientists as well as [...] Read more.

This paper reviews the interdisciplinary collaboration between Environmental Sciences and Statistics. The usage of statistical methods as a problem-solving tool for handling environmental problems is the key element of this approach. This paper enhances a clear pavement for environmental scientists as well as quantitative researchers for their further collaborative learning with an analytical base. Full article

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