Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
F-distributionIn probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests. The F-distribution with d1 and d2 degrees of freedom is the distribution of where and are independent random variables with chi-square distributions with respective degrees of freedom and .
Ratio distributionA ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio of two normally distributed variables with zero mean.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Chi-squared distributionIn probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals.
Logistic distributionIn probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.
Gumbel distributionIn probability theory and statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or the minimum) of a number of samples of various distributions. This distribution might be used to represent the distribution of the maximum level of a river in a particular year if there was a list of maximum values for the past ten years. It is useful in predicting the chance that an extreme earthquake, flood or other natural disaster will occur.
Cork cambiumCork cambium (pl. cambia or cambiums) is a tissue found in many vascular plants as a part of the epidermis. It is one of the many layers of bark, between the cork and primary phloem. The cork cambium is a lateral meristem and is responsible for secondary growth that replaces the epidermis in roots and stems. It is found in woody and many herbaceous dicots, gymnosperms and some monocots (monocots usually lack secondary growth). It is one of the plant's meristems – the series of tissues consisting of embryonic disk (incompletely differentiated) cells from which the plant grows.
Compressive strengthIn mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile strength resists tension (being pulled apart). In the study of strength of materials, tensile strength, compressive strength, and shear strength can be analyzed independently.
WoodWood is a structural tissue found in the stems and roots of trees and other woody plants. It is an organic material - a natural composite of cellulose fibers that are strong in tension and embedded in a matrix of lignin that resists compression. Wood is sometimes defined as only the secondary xylem in the stems of trees, or it is defined more broadly to include the same type of tissue elsewhere such as in the roots of trees or shrubs. In a living tree it performs a support function, enabling woody plants to grow large or to stand up by themselves.
Ultimate tensile strengthUltimate tensile strength (also called UTS, tensile strength, TS, ultimate strength or in notation) is the maximum stress that a material can withstand while being stretched or pulled before breaking. In brittle materials the ultimate tensile strength is close to the yield point, whereas in ductile materials the ultimate tensile strength can be higher. The ultimate tensile strength is usually found by performing a tensile test and recording the engineering stress versus strain.
Bark (botany)Bark is the outermost layers of stems and roots of woody plants. Plants with bark include trees, woody vines, and shrubs. Bark refers to all the tissues outside the vascular cambium and is a nontechnical term. It overlays the wood and consists of the inner bark and the outer bark. The inner bark, which in older stems is living tissue, includes the innermost layer of the periderm. The outer bark on older stems includes the dead tissue on the surface of the stems, along with parts of the outermost periderm and all the tissues on the outer side of the periderm.
Strength of materialsThe field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.
CambiumA cambium (plural cambia or cambiums), in plants, is a tissue layer that provides partially undifferentiated cells for plant growth. It is found in the area between xylem and phloem. A cambium can also be defined as a cellular plant tissue from which phloem, xylem, or cork grows by division, resulting (in woody plants) in secondary thickening. It forms parallel rows of cells, which result in secondary tissues. There are several distinct kinds of cambium found in plant stems and roots: Cork cambium, a tissue found in many vascular plants as part of the periderm.
Specific strengthThe specific strength is a material's (or muscle's) strength (force per unit area at failure) divided by its density. It is also known as the strength-to-weight ratio or strength/weight ratio or strength-to-mass ratio. In fiber or textile applications, tenacity is the usual measure of specific strength. The SI unit for specific strength is Pa⋅m3/kg, or N⋅m/kg, which is dimensionally equivalent to m2/s2, though the latter form is rarely used.
Vascular cambiumThe vascular cambium is the main growth tissue in the stems and roots of many plants, specifically in dicots such as buttercups and oak trees, gymnosperms such as pine trees, as well as in certain other vascular plants. It produces secondary xylem inwards, towards the pith, and secondary phloem outwards, towards the bark. In herbaceous plants, it occurs in the vascular bundles which are often arranged like beads on a necklace forming an interrupted ring inside the stem.
Vascular tissueVascular tissue is a complex conducting tissue, formed of more than one cell type, found in vascular plants. The primary components of vascular tissue are the xylem and phloem. These two tissues transport fluid and nutrients internally. There are also two meristems associated with vascular tissue: the vascular cambium and the cork cambium. All the vascular tissues within a particular plant together constitute the vascular tissue system of that plant. The cells in vascular tissue are typically long and slender.
PhloemPhloem ('floʊ.əm, ) is the living tissue in vascular plants that transports the soluble organic compounds made during photosynthesis and known as photosynthates, in particular the sugar sucrose, to the rest of the plant. This transport process is called translocation. In trees, the phloem is the innermost layer of the bark, hence the name, derived from the Ancient Greek word φλοιός (phloiós), meaning "bark". The term was introduced by Carl Nägeli in 1858.
Plant stemA stem is one of two main structural axes of a vascular plant, the other being the root. It supports leaves, flowers and fruits, transports water and dissolved substances between the roots and the shoots in the xylem and phloem, stores nutrients, and produces new living tissue. The stem can also be called halm or haulm or culms. The stem is normally divided into nodes and internodes: The nodes hold one or more leaves, as well as buds which can grow into branches (with leaves, conifer cones, or flowers).
