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Modeling to Factor Productivity of the United Kingdom Food Chain: Using a New Lifetime-Generated Family of Distributions

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  • Salem A. Alyami

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia)

  • Ibrahim Elbatal

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    These authors contributed equally to this work.)

  • Naif Alotaibi

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    These authors contributed equally to this work.)

  • Ehab M. Almetwally

    (Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt
    Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
    These authors contributed equally to this work.)

  • Mohammed Elgarhy

    (The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Egypt
    These authors contributed equally to this work.)

Abstract

This article proposes a new lifetime-generated family of distributions called the sine-exponentiated Weibull-H (SEW-H) family, which is derived from two well-established families of distributions of entirely different nature: the sine-G (S-G) and the exponentiated Weibull-H (EW-H) families. Three new special models of this family include the sine-exponentiated Weibull exponential (SEWE x ), the sine-exponentiated Weibull Rayleigh (SEWR) and sine-exponentiated Weibull Burr X (SEWBX) distributions. The useful expansions of the probability density function (pdf) and cumulative distribution function (cdf) are derived. Statistical properties are obtained, including quantiles ( Q U ), moments ( M O ), incomplete M O ( I M O ), and order statistics ( O S ) are computed. Six numerous methods of estimation are produced to estimate the parameters: maximum likelihood ( M L ), least-square ( L S ), a maximum product of spacing ( M P R S P ), weighted L S ( W L S ), Cramér–von Mises ( C R V M ), and Anderson–Darling ( A D ). The performance of the estimation approaches is investigated using Monte Carlo simulations. The total factor productivity (TFP) of the United Kingdom food chain is an indication of the efficiency and competitiveness of the food sector in the United Kingdom. TFP growth suggests that the industry is becoming more efficient. If TFP of the food chain in the United Kingdom grows more rapidly than in other nations, it suggests that the sector is becoming more competitive. TFP, also known as multi-factor productivity in economic theory, estimates the fraction of output that cannot be explained by traditionally measured inputs of labor and capital employed in production. In this paper, we use five real datasets to show the relevance and flexibility of the suggested family. The first dataset represents the United Kingdom food chain from 2000 to 2019, whereas the second dataset represents the food and drink wholesaling in the United Kingdom from 2000 to 2019 as one factor of FTP; the third dataset contains the tensile strength of single carbon fibers (in GPa); the fourth dataset is often called the breaking stress of carbon fiber dataset; the fifth dataset represents the TFP growth of agricultural production for thirty-seven African countries from 2001–2010. The new suggested distribution is very flexible and it outperforms many known distributions.

Suggested Citation

  • Salem A. Alyami & Ibrahim Elbatal & Naif Alotaibi & Ehab M. Almetwally & Mohammed Elgarhy, 2022. "Modeling to Factor Productivity of the United Kingdom Food Chain: Using a New Lifetime-Generated Family of Distributions," Sustainability, MDPI, vol. 14(14), pages 1-28, July.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:14:p:8942-:d:868064
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    References listed on IDEAS

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    1. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2020. "On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
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