ShapiroWilksTest

Shapiro Wilks Univariate test for normality

https://en.wikipedia.org/wiki/Shapiro%E2%80%93Wilk_test

See: https://ww2.mathworks.cn/matlabcentral/mlc-downloads/downloads/submissions/13964/versions/2/previews/swtest.m/index.html

as well as: https://github.com/wch/r-source/blob/trunk/src/library/stats/src/swilk.c

Both reference the AS R94 article on the shapiro wilk normality test. The R source version swilk.c is converted from the fortran implementation of that algorithm. The matlab source being a DSL is much easier to read through. However in both cases the coefficients of the polynomials are provided in tables and these are used in the expansion when calculating the a_i coefficients in the statistic.

In order to provide an implementation, the same constant coefficients will be used. However simplification of the C version is attempted with heavy influence from the approach taken in matlab.

Linear Supertypes

StatisticalTest, AnyRef, Any

Instance Constructors

new ShapiroWilksTest(series: Seq[Double])

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def asInstanceOf[T0]: T0

Definition Classes
Any
val c1: Seq[Double]
val c2: Seq[Double]
val c3: Seq[Double]
val c4: Seq[Double]
val c5: Seq[Double]
val c6: Seq[Double]
val c7: Seq[Double]
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
def computeStat(): (Double, Double)

Compute the critical value of the test statistic.
Compute the critical value of the test statistic.
returns
Returns a tuple (critical value x p value)
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → Any
def indexed(set: Seq[Double]): Seq[(Int, Double)]
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def mQuantiles(n: Int): DenseVector[Double]

approximate the mean of ith order statistics for quantiles 1:n
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
val norm: Normal

normal distribution.
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def ordered(): Seq[Double]

the ordered function.
val series: Seq[Double]
def shapiroFrancia(x: Seq[Double]): (Double, Double)

Compute the shapiro francia statistic and the corresponding pvalue
Compute the shapiro francia statistic and the corresponding pvalue
returns
tuple of (critical value x p value)
def shapiroWilks(x: Seq[Double]): (Double, Double)

Compute the shapiro wilks statistic and corresponding pvalue
Compute the shapiro wilks statistic and corresponding pvalue
returns
tuple of (critival value x p value)
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def test(alpha: Double): TestResult

Definition Classes
ShapiroWilksTest → StatisticalTest
def toString(): String

Definition Classes
AnyRef → Any
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
def zeros(n: Int): Seq[Double]

Related Docs: object ShapiroWilksTest | package analysis

class ShapiroWilksTest extends StatisticalTest

Instance Constructors

new ShapiroWilksTest(series: Seq[Double])

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

val c1: Seq[Double]

val c2: Seq[Double]

val c3: Seq[Double]

val c4: Seq[Double]

val c5: Seq[Double]

val c6: Seq[Double]

val c7: Seq[Double]

def clone(): AnyRef

def computeStat(): (Double, Double)

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

def indexed(set: Seq[Double]): Seq[(Int, Double)]

final def isInstanceOf[T0]: Boolean

def mQuantiles(n: Int): DenseVector[Double]

final def ne(arg0: AnyRef): Boolean

val norm: Normal

final def notify(): Unit

final def notifyAll(): Unit

def ordered(): Seq[Double]

val series: Seq[Double]

def shapiroFrancia(x: Seq[Double]): (Double, Double)

def shapiroWilks(x: Seq[Double]): (Double, Double)

final def synchronized[T0](arg0: ⇒ T0): T0

def test(alpha: Double): TestResult

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

def zeros(n: Int): Seq[Double]

Inherited from StatisticalTest

Inherited from AnyRef

Inherited from Any

Ungrouped