New Probability Distributions in Astrophysics: V. The Truncated Weibull Distribution

Application of Weibull distribution in a generalized way to estimate wind potential cannot always be advisable. The novelty of this work is to estimate wind potential using Normal probability density function. A comparison of five probability distributions namely Normal, Gamma, Chi-Squared, Weibull, and Rayleigh was done using three performance evaluation criteria. Four years (2015–2018) hourly wind data at 50 m height at five stations near the coastline of Pakistan was used. It was found that normal distribution gives the best fit at each of these stations and against each evaluation criterion followed by Weibull distribution while Rayleigh distribution gives the poorest fit. Further energy generation by fifteen turbine models was calculated and GE 45.7 was found the best in terms of amount of energy generation and capacity factors while Vestas V42 shows the worst. However, GE/1.5 SL is the most economical while Vestas V63 is the least. Among five locations, Shahbandar is the best potential site while Manora is the least.

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Effect of water absorption on the Weibull distribution of fatigue test in jute-reinforced polyester composite materials

Advanced Composites Letters ◽

10.1177/0963693519853833 ◽

2019 ◽

Vol 28 ◽

pp. 096369351985383 ◽

Cited By ~ 2

Author(s):

Djamel Djeghader ◽

Bachir Redjel

Keyword(s):

Composite Materials ◽

Weibull Distribution ◽

Probability Distributions ◽

Correlation Coefficients ◽

Statistical Correlation ◽

Polyester Composite ◽

Polyester Matrix ◽

Number Of Cycles ◽

Cycles To Failure ◽

Two Parameter

Composite materials have been manufactured using bidirectional jute yarn in a polyester matrix. The manufactured composite has been subjected to water aging for various times of immersion (90, 180, and 270 days). A significant decrease of fatigue strength has been observed during water aging. The number of cycles to failure of the aged and nonaged specimens were correlated using the two-parameter Weibull distribution function to determine the probability of failure and plot the S–N curves at different reliability levels. The results have shown that the two-parameter Weibull distribution describes the fatigue life probability distributions of jute-reinforced polyester composite material with highly significant statistical correlation coefficients.

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Fitting of Probability Distribution on the Post-Monsoon Rainfall of Different Locations in Bangladesh

Environment and Natural Resources Research ◽

10.5539/enrr.v9n2p27 ◽

2019 ◽

Vol 9 (2) ◽

pp. 27

Author(s):

Md. Habibur Rahman

Keyword(s):

Probability Distribution ◽

Weibull Distribution ◽

Gamma Distribution ◽

Goodness Of Fit ◽

Monsoon Rainfall ◽

Probability Distributions ◽

Monsoon Precipitation ◽

Post Monsoon

Different probability distributions of post-monsoon rainfall of different locations in Bangladesh are fitted. It is found that, for the data, Weibull distribution for Barisal, Bogra, Chittagong, Comilla, Cox's Bazar, Faridpur, Jessore, Khulna, Maijdi Court, Mymensingh, Satkhira, and Sylhet; the Gamma distribution for Dhaka, Ishurdi, Rangamati, Rangpur, and Srimangal based on graphical assessment and goodness-of-fit criterion. In this study, different probability distributions have been fitted for the data of post-monsoon precipitation for 17 different locations in Bangladesh over the period 1961-2014.

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The Transmuted Generalized Inverse Weibull Distribution

Austrian Journal of Statistics ◽

10.17713/ajs.v43i2.28 ◽

2014 ◽

Vol 43 (2) ◽

pp. 119-131 ◽

Cited By ~ 7

Author(s):

Faton Merovci ◽

Ibrahim Elbatal ◽

Alaa Ahmed

Keyword(s):

Weibull Distribution ◽

Generalized Inverse ◽

Probability Distributions ◽

Information Matrix ◽

Real Data ◽

Moment Generating Function ◽

Model Parameters ◽

Data Set ◽

Method Of Maximum Likelihood ◽

Inverse Weibull Distribution

A generalization of the generalized inverse Weibull distribution the so-called transmuted generalized inverse Weibull distribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking the generalized inverseWeibull distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the flexibility of the transmuted version versus the generalized inverse Weibull distribution.

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Estimasi Parameter Distribusi Weibull Dan Aplikasinya pada Pengendalian Mutu Dengan Memanfaatkan Kuantil

Unisda Journal of Mathematics and Computer Science (UJMC) ◽

10.52166/ujmc.v5i01.1473 ◽

2019 ◽

Vol 5 (01) ◽

pp. 9-15

Author(s):

Cecilia Novianti Salsinha

Keyword(s):

Maximum Likelihood ◽

Weibull Distribution ◽

Control Charts ◽

Probability Distributions ◽

Likelihood Estimation ◽

Control Limit ◽

Statistical Process ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Distribution Parameters

Abstract. Weibull distribution is one of the continuous probability distributions. As the other distributions, Weibull distribution is also characterized by Mean, Variance and Moment Generation Function. The advantage of this distribution compared to other distributions is its flexibility, that is, this distribution can change to another distribution such as an exponential distribution depending on the value of the selected distribution parameters, namely scale parameters and form parameters. From the distribution graph, it can be shown that, the flexibility will appear very clear. One application of the Weibull distribution is in statistical process control. Because not all data is normally distributed, the Shewhart control chart cannot be used. One way to solve this problem is that the data is analyzed with Weibull control charts by utilizing quantiles, namely 0.00135, 0.5 and 0.99865. Quantile 0.00135 is the bottom quintile used to form the Lower Control Limit, the Middle Line is the median of the data, which is 0.5 which replaces the average and the last to form the Upper Control Limit the top quintile is 0.99865. By generating 200 data with Weibull distribution, if the data is analyzed by Shewhart control charts then there is a lot of data that is outside the control limit so it will be concluded that the graph is out of control. Therefore, if the data is not from a Normal distribution, the use of Shewhart control charts is not recommended. Keywords: Weibull Distribution, Maximum Likelihood Estimation (MLE), Quality Control, Weibull Control Charts Abstrak. Distribusi Weibull merupakan salah satu distribusi probabilitas kontinu. Sama halnya dengan distribusi lainnya, distribusi Weibull pun dicirikan dengan Mean, Variansi dan Fungsi Pembangkit Momen. Kelebihan distribusi ini dibandingkan dengan distribusi lainnya adalah fleksibilitasnya, yaitu distribusi ini dapat berubah menjadi distribusi lain seperti distribusi eksponensial tergantung pada nilai parameter distribusi yang dipilih yaitu parameter skala dan parameter bentuk. Jika dilihat dari grafik distribusinya maka akan tampak sangat jelas fleksibilitas tersebut. Salah satu aplikasi dari distribusi Weibull yaitu dalam pengendalian proses statistik. Oleh karena tidak semua data berdistribusi normal maka grafik pengendali Shewhart tidak dapat digunakan. Salah satu cara menyelesaikan masalah tersebut adalah data dianalisis dengan grafik pengendali Weibull dengan memanfaatkan kuantil-kuantil yaitu 0,00135, 0,5 dan 0,99865. Kuantil 0,00135 adalah kuantil bawah yang digunakan untuk membentuk Batas Pengendali Bawah, Garis Tengah adalah median dari data yaitu 0,5 yang menggantikan rata-rata dan untuk membentuk Batas Pengendali Atas digunakan kuantil atas yaitu 0,99865. Dengan membangkitkan data sebanyak 200 data berdistribusi Weibull, jika data tersebut dianalisis dengan grafik pengendali Shewhart maka terdapat banyak data yang berada diluar batas pengendali sehingga akan disimpulkan bahwa grafik tak terkendali. Oleh karena itu, jika data bukan berasal dari distribusi Normal, penggunaan grafik pengendali Shewhart tidak disarankan. Kata Kunci: Distribusi Weibull, Estimasi Maximum Likelihood, Pengendalian Mutu, Grafik Pengendali Weibull

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A Novel Approach to Increase the Goodness of Fits with an Application to Real and Simulated Data Sets

Mathematical Problems in Engineering ◽

10.1155/2021/9717872 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Muhammad Farooq ◽

Qamruz zaman ◽

Muhammad Ijaz ◽

Said Farooq Shah ◽

Mutua Kilai

Keyword(s):

Weibull Distribution ◽

Extreme Values ◽

Probability Distributions ◽

Probability Model ◽

Simulated Data ◽

Real Data ◽

Data Sets ◽

Estimation Of Parameters ◽

Novel Approach ◽

Lifetime Analysis

In practice, the data sets with extreme values are possible in many fields such as engineering, lifetime analysis, business, and economics. A lot of probability distributions are derived and presented to increase the model flexibility in the presence of such values. The current study also focuses on investigations to derive a new probability model New Flexible Family (NFF) of distributions. The significance of NFF is carried out using the Weibull distribution called New Flexible Weibull distribution or in short NFW. Various mathematical properties of NFW have been discussed including the estimation of parameters and entropy measures. Two real data sets with extreme values and a simulation study have been conducted so as to delineate the importance of NFW. Furthermore, NFW is compared with other existing probability distributions; numerically, it has been observed that the new mechanism of producing the lifetime probability distributions plays a significant role in making predictions about the population than others using the data sets with extreme values.

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A class of probability distributions for application to non-negative annual maxima

10.5194/hess-2017-198 ◽

2017 ◽

Author(s):

Earl Bardsley

Keyword(s):

Weibull Distribution ◽

Probability Distributions ◽

Random Variables ◽

Extreme Value Distribution ◽

Extreme Value ◽

Value Distribution ◽

Asymptotic Distributions ◽

Generalized Extreme Value Distribution ◽

Extreme Value Distributions ◽

Specific Distribution

Abstract. Many environmental variables of interest as potential hazards take on only positive values, such a wind speed or river discharge. While recognising that primary interest is for largest extremes, it is desirable that distributions of maxima for design purposes should be subject to similar bounds as the physical variable concerned. A modified univariate extreme value argument defines a set of distributions, all bounded below at zero, with potential for application to annual maxima. Let f(x) be a probability distribution over the range, 0 ≤ x ≤ ω, where 0 0, c > 0 where ɛ = g(ω) and ɛ, ɑ, and c are respectively location, scale, and shape parameters. The distribution F(y) holds generally as an extreme value expression for sufficiently large N, irrespective of which of the three possible asymptotic extreme value distributions of sample maxima holds for X*. Therefore, the limit Weibull distribution for, say, Y* = X*−1 has no less validity as a single expression for obtaining exceedance probabilities than the generalized extreme value distribution applied directly to X*. If follows that a class of probability distributions for possible use with positive-valued annual maxima can be defined from the application of the inverse function g−1 to Weibull random variables for ɛ ≥ 0. All distributions so obtained are defined over the range 0 ≤ x ≤ ω, which actually excludes all of the asymptotic extreme value distributions of maxima except for the special case of the Type 2 extreme value distribution with location parameter at zero. It is to be expected, however, that the asymptotic distributions will sometimes hold to a high level of approximation within the 0, ω interval. No specific distribution is advocated for annual maxima application because concern here is only with drawing attention to the existence of the distribution class. The transformation approach is illustrated with respect the distribution of reciprocals of random variables generated from a 3-parameter Weibull distribution with ɛ ≥ 0.

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Brownian motion with quadratic killing and some implications

Journal of Applied Probability ◽

10.1017/s0021900200116079 ◽

1986 ◽

Vol 23 (04) ◽

pp. 893-903 ◽

Cited By ~ 2

Author(s):

Michael L. Wenocur

Keyword(s):

Brownian Motion ◽

Weibull Distribution ◽

Special Function ◽

Function Theory ◽

Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

International Astronomical Union Colloquium ◽

10.1017/s0252921100014718 ◽

1997 ◽

Vol 161 ◽

pp. 197-201 ◽

Cited By ~ 1

Author(s):

Duncan Steel

Keyword(s):

Probability Distributions ◽

Regions Of Interest ◽

Significant Fraction ◽

Organic Chemicals ◽

Impact Speed ◽

The Mean ◽

The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

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